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Algebra 2 Worksheets with answer keys

Enjoy these free printable math worksheets . Each one has model problems worked out step by step, practice problems, as well as challenge questions at the sheets end. Plus each one comes with an answer key.

  • Absolute Value Equations
  • Simplify Imaginary Numbers
  • Adding and Subtracting Complex Numbers
  • Multiplying Complex Numbers
  • Dividing Complex Numbers
  • Dividing Complex Number (advanced)
  • End of Unit, Review Sheet
  • Exponential Growth (no answer key on this one, sorry)
  • Compound Interest Worksheet #1 (no logs)
  • Compound Interest Worksheet (logarithms required)
  • Simplify Rational Exponents
  • Solve Equations with Rational Exponents
  • Solve Equations with variables in Exponents
  • Factor by Grouping
  • 1 to 1 functions
  • Evaluating Functions
  • Composition of Functions
  • Inverse Functions
  • Operations with Functions
  • Functions Review Worksheet
  • Product Rule of Logarithms
  • Power Rule of Logarithms
  • Quotient Rule of Logarithms
  • Logarithmic Equations Worksheet
  • Dividing Polynomials Worksheet
  • Solve Quadratic Equations by Factoring
  • Solve Quadratic Equations by Completing the Square
  • Quadratic formula Worksheet (real solutions)
  • Quadratic Formula Worksheet (complex solutions)
  • Quadratic Formula Worksheet (both real and complex solutions)
  • Discriminant Worksheet
  • Sum and Product of Roots
  • Radical Equations
  • Rationalizing the Denominator
  • Simplify Rational Expressions Worksheet
  • Dividing Rational Expressions
  • Multiplying Rational Expressions
  • Adding and Subtracting Rational Expressions (with like denominators)
  • Adding and Subtracting Ratioal Expressions with Unlike Denominators
  • Mixed Review on Rational Expressions

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Surface area of a Cylinder

Factoring in Algebra

Numbers have factors :

And expressions (like x 2 +4x+3 ) also have factors:

Factoring (called " Factorising " in the UK) is the process of finding the factors :

Factoring: Finding what to multiply together to get an expression.

It is like "splitting" an expression into a multiplication of simpler expressions.

Example: factor 2y+6

Both 2y and 6 have a common factor of 2:

So we can factor the whole expression into:

2y+6 = 2(y+3)

So 2y+6 has been "factored into" 2 and y+3

Factoring is also the opposite of Expanding :

Common Factor

In the previous example we saw that 2y and 6 had a common factor of 2

But to do the job properly we need the highest common factor , including any variables

Example: factor 3y 2 +12y

Firstly, 3 and 12 have a common factor of 3 .

So we could have:

3y 2 +12y = 3(y 2 +4y)

But we can do better!

3y 2 and 12y also share the variable y .

Together that makes 3y :

  • 3y 2 is 3y × y
  • 12y is 3y × 4

3y 2 +12y = 3y(y+4)

Check: 3y(y+4) = 3y × y + 3y × 4 = 3y 2 +12y

More Complicated Factoring

Factoring can be hard .

The examples have been simple so far, but factoring can be very tricky.

Because we have to figure what got multiplied to produce the expression we are given!

Experience Helps

With more experience factoring becomes easier.

Example: Factor 4x 2 − 9

Hmmm... there don't seem to be any common factors.

But knowing the Special Binomial Products gives us a clue called the "difference of squares" :

Because 4x 2 is (2x) 2 , and 9 is (3) 2 ,

So we have:

4x 2 − 9 = (2x) 2 − (3) 2

And that can be produced by the difference of squares formula:

(a+b)(a−b) = a 2 − b 2

Where a is 2x, and b is 3.

So let us try doing that:

(2x+3)(2x−3) = (2x) 2 − (3) 2 = 4x 2 − 9

So the factors of 4x 2 − 9 are (2x+3) and (2x−3) :

Answer: 4x 2 − 9 = (2x+3)(2x−3)

How can you learn to do that? By getting lots of practice, and knowing "Identities"!

Remember these Identities

Here is a list of common "Identities" (including the "difference of squares" used above).

It is worth remembering these, as they can make factoring easier.

There are many more like those, but those are the most useful ones.

The factored form is usually best.

When trying to factor, follow these steps:

  • "Factor out" any common terms
  • See if it fits any of the identities, plus any more you may know
  • Keep going till you can't factor any more

There are also Computer Algebra Systems (called "CAS") such as Axiom, Derive, Macsyma, Maple, Mathematica, MuPAD, Reduce and others that can do factoring.

More Examples

Experience does help, so here are more examples to help you on the way:

Example: w 4 − 16

An exponent of 4? Maybe we could try an exponent of 2:

w 4 − 16 = (w 2 ) 2 − 4 2

Yes, it is the difference of squares

w 4 − 16 = (w 2 + 4)(w 2 − 4)

And "(w 2 − 4)" is another difference of squares

w 4 − 16 = (w 2 + 4)(w+ 2)(w− 2)

That is as far as I can go (unless I use imaginary numbers)

Example: 3u 4 − 24uv 3

Remove common factor "3u":

3u 4 − 24uv 3 = 3u(u 3 − 8v 3 )

Then a difference of cubes:

3u 4 − 24uv 3 = 3u(u 3 − (2v) 3 )

= 3u(u−2v)(u 2 +2uv+4v 2 )

That is as far as I can go.

Example: z 3 − z 2 − 9z + 9

Try factoring the first two and second two separately:

z 2 (z−1) − 9(z−1)

Wow, (z-1) is on both, so let us use that:

(z 2 −9)(z−1)

And z 2 −9 is a difference of squares

(z−3)(z+3)(z−1)

Now get some more experience:

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  • Pre Algebra Order of Operations Factors & Primes Fractions Long Arithmetic Decimals Exponents & Radicals Ratios & Proportions Percent Modulo Number Line Mean, Median & Mode
  • Algebra Equations Inequalities System of Equations System of Inequalities Basic Operations Algebraic Properties Partial Fractions Polynomials Rational Expressions Sequences Power Sums Interval Notation Pi (Product) Notation Induction Logical Sets Word Problems
  • Pre Calculus Equations Inequalities Scientific Calculator Scientific Notation Arithmetics Complex Numbers Polar/Cartesian Simultaneous Equations System of Inequalities Polynomials Rationales Functions Arithmetic & Comp. Coordinate Geometry Plane Geometry Solid Geometry Conic Sections Trigonometry
  • Calculus Derivatives Derivative Applications Limits Integrals Integral Applications Integral Approximation Series ODE Multivariable Calculus Laplace Transform Taylor/Maclaurin Series Fourier Series Fourier Transform
  • Functions Line Equations Functions Arithmetic & Comp. Conic Sections Transformation
  • Linear Algebra Matrices Vectors
  • Trigonometry Identities Proving Identities Trig Equations Trig Inequalities Evaluate Functions Simplify
  • Statistics Mean Geometric Mean Quadratic Mean Average Median Mode Order Minimum Maximum Probability Mid-Range Range Standard Deviation Variance Lower Quartile Upper Quartile Interquartile Range Midhinge Standard Normal Distribution
  • Physics Mechanics
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  • Finance Simple Interest Compound Interest Present Value Future Value
  • Economics Point of Diminishing Return
  • Conversions Roman Numerals Radical to Exponent Exponent to Radical To Fraction To Decimal To Mixed Number To Improper Fraction Radians to Degrees Degrees to Radians Hexadecimal Scientific Notation Distance Weight Time
  • Pre Algebra
  • One-Step Addition
  • One-Step Subtraction
  • One-Step Multiplication
  • One-Step Division
  • One-Step Decimals
  • Two-Step Integers
  • Two-Step Add/Subtract
  • Two-Step Multiply/Divide
  • Two-Step Fractions
  • Two-Step Decimals
  • Multi-Step Integers
  • Multi-Step with Parentheses
  • Multi-Step Rational
  • Multi-Step Fractions
  • Multi-Step Decimals
  • Solve by Factoring
  • Completing the Square
  • Quadratic Formula
  • Biquadratic
  • Logarithmic
  • Exponential
  • Rational Roots
  • Floor/Ceiling
  • Equation Given Roots
  • Newton Raphson
  • Substitution
  • Elimination
  • Cramer's Rule
  • Gaussian Elimination
  • System of Inequalities
  • Perfect Squares
  • Difference of Squares
  • Difference of Cubes
  • Sum of Cubes
  • Polynomials
  • Distributive Property
  • FOIL method
  • Perfect Cubes
  • Binomial Expansion
  • Negative Rule
  • Product Rule
  • Quotient Rule
  • Expand Power Rule
  • Fraction Exponent
  • Exponent Rules
  • Exponential Form
  • Logarithmic Form
  • Absolute Value
  • Rational Number
  • Powers of i
  • Partial Fractions
  • Is Polynomial
  • Leading Coefficient
  • Leading Term
  • Standard Form
  • Complete the Square
  • Synthetic Division
  • Linear Factors
  • Rationalize Denominator
  • Rationalize Numerator
  • Identify Type
  • Convergence
  • Interval Notation
  • Pi (Product) Notation
  • Boolean Algebra
  • Truth Table
  • Mutual Exclusive
  • Cardinality
  • Caretesian Product
  • Age Problems
  • Distance Problems
  • Cost Problems
  • Investment Problems
  • Number Problems
  • Percent Problems
  • Addition/Subtraction
  • Multiplication/Division
  • Dice Problems
  • Coin Problems
  • Card Problems
  • Pre Calculus
  • Linear Algebra
  • Trigonometry
  • Conversions

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  • factor\:x^{2}-5x+6
  • factor\:(x-2)^2-9
  • factor\:2x^2-18
  • factor\:5a^2-30a+45
  • factor\:x^6-2x^4-x^2+2
  • factor\:2x^5+x^4-2x-1
  • What is the sum of cubes formula?
  • The sum of cubes formula is a³ + b³ = (a+b)(a² - ab + b²)
  • What is the difference of squares formula?
  • The difference of squares formula is a² - b² = (a+b)(a-b)
  • What is the difference of cubes formula?
  • The difference of cubes formula is a³ - b³ = (a-b)(a² + ab + b²)
  • How do you solve factoring by greatest common monomial factor?
  • To factor by greatest common monomial factor, find the greatest common monomial factor among the terms of the expression and then factor it out of each term.
  • How do you factor a monomial?
  • To factor a monomial, write it as the product of its factors and then divide each term by any common factors to obtain the fully-factored form.
  • How do you factor a binomial?
  • To factor a binomial, write it as the sum or difference of two squares or as the difference of two cubes.
  • How do you factor a trinomial?
  • To factor a trinomial x^2+bx+c find two numbers u, v that multiply to give c and add to b. Rewrite the trinomial as the product of two binomials (x-u)(x-v)
  • How to find LCM with the listing multiples method?
  • To find the LCM of two numbers using the listing multiples method write down the multiples of the first number and write down the multiples of the second number. Find the smallest number that is a multiple of both of the numbers.

factor-calculator

  • Middle School Math Solutions – Polynomials Calculator, Factoring Quadratics Just like numbers have factors (2×3=6), expressions have factors ((x+2)(x+3)=x^2+5x+6). Factoring is the process... Read More

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Numbers 1 – 20 Worksheets For Kindergarten Pictures

Numbers 1 – 20 Worksheets For Kindergarten With Pictures – Free Printable Numbers Worksheets

Numbers 1 – 20 Worksheets For Kindergarten With Pictures: Again we have come up with another set of number series worksheets. If you are a parent, teacher, or homeschooler this type of Numbers 1- 20 activity set will help students, preschoolers, and kindergarteners understand the concepts of maths easily.

But While preparing Worksheets for those young children they should be interactive and fun way. If you see our worksheets there are many colorful pictures that we have given along with numbers 1- 20.

Help your kids have fun learning maths with our Numbers 1 – 20 Worksheets Free Printables .

Counting Practice Numbers 1 – 20 Activity Sheets PDF Online & Offline

We all know that Numbers are fundamental in every Child’s life. Check out the worksheets that you think will work for you and then download that particular worksheet for free of cost and take the printout.

Activities that are provided in the Worksheets help students have fun by matching numbers, counting dots, and counting dolls, fruits, and others. These worksheets help curious young minds improve their thinking skills.

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As your child grows up, Numbers are essential to learning as they will be very useful in upcoming classes. The below worksheets help to recognize numbers, find numbers in balloons along with colors, and help children learn interestingly.

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Writing Numbers 1-20 Worksheets PDF Free Download

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Numbers 1 – 20 Worksheets For Kindergarten With Pictures

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It is an easy way to make your students or children comfortable with maths. You can visit our website @ Worksheetsbuddy.com for other worksheet pages.

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  1. PDF Factoring Trinomials (a > 1) Date Period

    Factor each completely. 1) 3 p2 − 2p − 5 2) 2n2 + 3n − 9 3) ... Infinite Algebra 1 Name_____ ... .L L EA El KlU yr ViOgWhQtNsO Srkews2eqr SvAe6d w.h 7 SMfa OdWeU Zw8iAtnhL kI EnyfWi7nVigtMei MATlXgie 1b 7rea c T1U.1 Worksheet by Kuta Software LLC 9) 15 n2 − 27 n − 6 3(5n + 1)(n − 2) 10) 5x2 − 18 x + 9 (5x − 3)(x − 3)

  2. PDF CP Algebra 2 Unit 2-1: Factoring and Solving Quadratics WORKSHEET PACKET

    Learning Targets: LT 0 Unit 2-1 CPA2 Name __________________ Pd _______ I can add, subtract and multiply polynomial expressions Use and attach another sheet of paper for work. Write the polynomial in standard form. Then state it's degree. 17. 14 + x + 13x2 3 3 x2 − x 5 2 18. 19. -1 +x2 + 6x3 20. x3 + 5x - 2x2 + 2 € 21. -3x2 + 3 - x3

  3. PDF Factoring Quadratic Expressions

    Factor each completely. 1) n2 + 8 n + 12 3) k2 − 2 k − 24 5) p2 − 16 p + 60 7) v2 + 4 v − 32 9) x2 + 16 x + 60 11) 5 n2 + 43 n − 18 13) 2 n2 − 9

  4. PDF Factoring Trinomials (a = 1) Date Period

    Factor each completely. 1) b2 + 8b + 7 2) n2 − 11 n + 10 3) m2 + m − 90 4) ... (v + 1)-2-Create your own worksheets like this one with Infinite Algebra 1. Free trial available at KutaSoftware.com. Title: Factoring 1 Author: Mike Created Date:

  5. Algebra 2 Worksheets (pdf) with answer keys

    Factoring Worksheets Factor by Grouping Functions and Relations 1 to 1 functions Evaluating Functions Composition of Functions Inverse Functions Operations with Functions Functions Review Worksheet Logarithm Worksheets Product Rule of Logarithms Power Rule of Logarithms Quotient Rule of Logarithms Logarithmic Equations Worksheet

  6. Solving quadratic equations by factoring (article)

    What you will learn in this lesson So far you have solved linear equations, which include constant terms—plain numbers—and terms with the variable raised to the first power, x 1 = x . You may have also solved some quadratic equations, which include the variable raised to the second power, by taking the square root from both sides.

  7. PDF Infinite Algebra 2

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  8. PDF Algebra II Factoring Unit

    Algebra II Factoring Unit Factoring I: Common monomials and factoring x2 + bx +c EX 1: Find the GCF of 18x2 and 24x: GCF = Greatest Common Factor EX 2: Factor: 12x2y3 + 6xy4 - 24xy5 What is common to every item in there? _____ Put that on the outside and "pull it out" of every term -- divide. Remainder goes inside the parenthesis.

  9. Factoring by grouping (article)

    Example: Factor 6x^2 + 19x + 10. 6*10 = 60, so we need to find two numbers that add to 19 and multiply to give 60. These numbers (after some trial and error) are 15 and 4. So split up 19x into 15x + 4x (or 4x + 15x), then factor by grouping: 6x^2 + 19x + 10 = 6x^2 + 15x + 4x + 10.

  10. PDF 7.4 Factor and Solving Polynomial Equations Student

    1 Recall Factoring: Factoring out a GCF: Factoring trinomials: a. 2!! − 4!! + 12! b. ... Worksheet by Kuta Software LLC Practice 7.4 Factor completely by factoring out a GCF, then factoring the remaining trinomial. ... Algebra Skillz GRAPH Below, the graph of !!=|!−1|+2 is sketched in bold. Its parent function

  11. PDF Factoring with GCF

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  12. Factoring in Algebra

    Factors Numbers have factors: And expressions (like x2+4x+3) also have factors: Factoring Factoring (called " Factorising " in the UK) is the process of finding the factors: Factoring: Finding what to multiply together to get an expression. It is like "splitting" an expression into a multiplication of simpler expressions. Example: factor 2y+6

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    The Algebra 2 course, often taught in the 11th grade, covers Polynomials; Complex Numbers; Rational Exponents; Exponential and Logarithmic Functions; Trigonometric Functions; Transformations of Functions; Rational Functions; and continuing the work with Equations and Modeling from previous grades. Khan Academy's Algebra 2 course is built to deliver a comprehensive, illuminating, engaging, and ...

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  15. PDF Algebra I Practice A.SSE.A.2: Factoring Polynomials 1 www.jmap.org NAME:

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    Include Monomials Worksheet Answer Page. Now you are ready to create your Monomials Worksheet by pressing the Create Button. If You Experience Display Problems with Your Math Worksheet. This polynomials worksheet will produce problems for factoring quadratic expressions. You may select which type of polynomials to factor, and whether you want ...

  17. Mixed Factoring Practice 2

    Mixed Factoring Practice 2 - MathBitsNotebook (A1) Answer these questions pertaining to factoring. Only completely factored answers are deemed as correct. The answers from the helpers may, or may not, be correct. 1. Factor completely: 2x2 - 98. Choose:

  18. Factoring Calculator

    To factor a binomial, write it as the sum or difference of two squares or as the difference of two cubes. How do you factor a trinomial? To factor a trinomial x^2+bx+c find two numbers u, v that multiply to give c and add to b. Rewrite the trinomial as the product of two binomials (x-u) (x-v)

  19. Business or Farm Income Apportionment Formula (IAF) Worksheet

    Worksheet for Schedule CR, Line: 1 Line 1 is 1.000000. 2 Figure your apportionment factor. 3 Subtract Line 2 from Line 1. 4 Enter the amount of your business or farm income from Schedule CR, Column A. 5 Apportioned Income - Multiply Line 4 by the Line 3 decimal. Enter the result here and on the corresponding line on Schedule CR, Column B.

  20. PDF Factoring By Grouping

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    Chemistry. Discussion Worksheet 5 1) Solve for the activation energy, E a , and the orientation factor, A , using the following table k (M -1 s -1 ) T (K) 2.5 783 5.4 852 2) I 2 ⇄ 2I (fast) H 2 + 2I → 2HI (slow) Use the steady-state approximation to determine the rate of the reaction. Page 1 of 1. Uploaded by BaronWolverineMaster1072 on ...