These activity sheets give your students practice in working with polynomials, including factoring and simplifying.

Factoring in mathematics means breaking apart of a polynomial into a product of other polynomials. When you multiply these small polynomials, you get the original polynomial. Regardless of how many terms there are in a polynomial, you need to always check for the greatest common factor (GCF) first. The GCF is the biggest expression that will go into all of the terms. For trinomial, a polynomial with three terms - you can use the FOIL method for multiplying binomials backward. For binomials, look for the difference of squares, the difference of cubes, or the sum of cubes.

Factoring is used to solve many different types of problems. The skill itself does not do much or serve a great purpose, but it is essential for the final process. Factoring is kind of like a screw driver. If you to hold two boards together there are many way you could do it. You could use glue, a nail, even staples; but a screw is the most efficient tool to get the job done. That is factoring for you, the screws of the math world. Your students will use the following worksheets to practice working with polynomials. Students will also use the distributive property. Though formulas are presented, students should already be familiar with this material.



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Factoring Polynomials Worksheets

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Distributive Property and Perfect Squares Lesson

We will show students how to factor the given expression using the distributive property. You will work on: 7mn2 + 14(m2n)2 + 2(mn)3. We quick see that all terms can be factored.

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Lesson and Practice

Students will review how to use the distributive property to factorize. A sample problem is solved and two practice problems are provided.

Worksheet

Students will use the distributive property to factorize the expressions that are given. You get ten opportunities with this skill.

Practice

Complete the factorization process using perfect square formulas over this series of problems.

Drill

Factor each polynomial in two steps. First step should be to find the greatest common factor of the terms. Eight problems are provided.

Warm Up

Students will use the distributive property to factor a series of expressions. Three problems are provided.

Lesson

This worksheet explains how to factor your every day polynomials. A sample problem is solved, and two practice problems are provided.

Factoring Polynomials Worksheet

Students will get some practice factoring a series of expressions over ten problems are provided.

Practice

Students will practice factoring polynomials. You get ten cracks at them.

Review

The concept of how to factor polynomials is reviewed. A sample problem is solved and six practice problems are provided.

Quiz

Students will demonstrate their proficiency with the skills that we have been exploring. You will find ten practice exercises for you.

Skills Check

This sheet is an excellent way to either introduce or review this topic.

Lesson

This worksheet explains how to simplify basic algebraic fractional expressions. A sample problem is solved, and two practice problems are provided.

Simplify Algebraic Fractions Worksheet

We will work with algebraic fractions that all involve a quotient based solution. Ten problems are provided.

Practice

Students will practice simplifying algebraic expressions into a simple form. You will find ten practice exercises for you.

Review

The concept of working with algebraic fractions is reviewed. A sample problem is solved and six practice problems are provided.

Quiz

Students will demonstrate their ability with simplifying and ultimately solving algebraic fractions. You get ten opportunities with this skill.

Skills Check

This is super helpful for working with students as a class.

Lesson

This lesson will break down the following problem step by step: Write in the simplest form. (x3 + 5x2 + 11x + 6) / (x2+ 5x + 6)

Simplifying Rational Fractional Expressions Worksheet

Students will simplify rational fractional expressions. Ten problems are provided.

Practice

Students will help breakdown these fractional expressions up into digestable pieces. You will find ten practice exercises for you.

Review

: First, factorize each of the two polynomial, cancel out the common factor in both. (x-1)(x+1) is common in both cancel it. 1/(x-1) is left out and is answer.

Quiz

Students will demonstrate their proficiency with writing these expressions in the simplest form. Ten problems are provided.

Check

This is super helpful for determining the basis of the concepts that we are exploring.

Lesson

This worksheet explains how to factor polynomials top to bottom. A sample problem is solved.

Summary of Factoring Lesson and Practice

A diagram shows a rectangular land with swimming pool inside it. The length and width of swimming pool is 3 ft. Write a polynomial expression for the area of the remaining land?

Worksheet

Students will factor some very plain polynomials. You get ten opportunities with this skill.

Practice

We review the core fundamental skills here. Ten problems are provided.

Drill

More base problems for students to work on.

Warm Up

Find the expression for the area of the field in the given figure. What will be the area of the field if the length is decreased by 3? What will be the value of 'a' if, the area of the field is 36 sq. ft and the width is increased by 7?