# Rewrite by Factoring Worksheets

How to Rewrite a Number by Factoring - Factoring is the opposite of distributing. When distributing, you multiply a series of terms by a common factor. When factoring, you seek to find what a series of terms have in common and then take it away, dividing the common factor out from each term. Think of each term as a numerator and then find the same denominator for each. By factoring out, the factor is put outside the parentheses or brackets, and all the results of the divisions are left inside. The proper way to factor expression is to write the prime factorization of each of the numbers and look for the greatest common factor. A more practical and quicker way is to look for the largest factor that you can easily recognize. Factor it out and then see if the numbers within the parentheses need to be factored again. Repeat the division until the terms within the parentheses are relatively prime.

• ### Basic Lesson

Demonstrates how to find rewrite an expression by factoring. Also includes practice problems. Rewrite the expression by factoring. 4h + 4y The expression can be re-written as 4h = 4 x h and 4y = 4 x y We can quickly recognize that both terms contain the factor 4 in common in the given expression. The right hand side of the above equation is in factored form because it is a single term only. The expression does not consist of two or more parts which are connected by plus or minus signs. The factored expression above is mathematically equivalent to the original expression and is easily verified by multiplication.

• ### Intermediate Lesson

Asks students to rewrite larger expressions.

• ### Independent Practice 1

20 problems ask for the Rewrite by Factoring.

• ### Independent Practice 2

20 practice problems that review Rewrite by Factoring skills. The answers can be found below.

• ### Homework Worksheet

12 problems to reinforce the lessons and practice pages. An example is provided.

• ### Skill Quiz

10 problems that test rewriting expressions skills.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Al and Sal

Al plays golf every 6 days and Sal plays every 4. If they both played today, when will it happen again that they play on the same day? Multiply the common factors raised to the highest power and the factors not common and get the answer 12 days.