# Factoring Polynomials with Common Factors

Section 6.1 Factoring Polynomials with Common Factors
Read section 6.1, pages 322 – 326 and answer the following questions as you

1. What is factoring?

2. Circle all the polynomials below that are factored. How do you know
they are factored?

*Which of the expressions above are equivalent?

3. Explain how to find the greatest common factor of two monomials . If
it helps, use #4 as an example.

4. Find the greatest common factor of and

5. Factor out the greatest common factor from . How do you
know what to put in the parentheses ?

6. Factor the greatest common monomial factor from

7. Factor in two ways:

a. Factor out a common monomial factor of 3

b. Factor out a common monomial factor of –3

8. Give an example of a binomial whose greatest common factor is 5x.
Then, factor it.

9. Underline the common binomial factors in the following polynomials,
and then factor the binomials out. Some polynomials may not have a
common binomial factor, in which case you will not be able to factor it.

10. Factor by grouping

11. The area of a rectangle can be represented by the polynomial .
Find the dimensions of the rectangle. (Explain how you
know these must be the dimensions.)

12. Find a polynomial that factors as .

Section 6.2 Factoring Trinomials
Read section 6.2, pages 330 – 334 and answer the following questions as you

1. Warm up: find all pairs of numbers that multiply to 36.

2. FOIL each of the following expressions but do not combine like terms .
You are going to factor the results, so leave space.

3. Factor each of your answers in #1 by grouping. What do you notice
about the factored form and the original expression?

4. To factor the trinomial we must find two numbers whose
__________ is 7 and whose __________ is 6. What are the two

5. To factor the polynomial we must find two numbers whose
product is _____ and whose sum is ______. Factor the trinomial. FOIL to

6. In the ‘Guidelines for Factoring why must m and n have
unlike signs if c is negative ?

7. Factor

8. How do you know when you have factored completely?

9. Factor completely:

10. What do we call a trinomial that cannot be factored?

Section 6.3 Relations, Functions, and Graphs
Read section 6.3, pages 338 – 342 and answer the following questions as you

1. Read the objectives. What is different from what you have already
learned?

*Skip the first five examples since we will not use this method to factor. Go
right to the middle of page 341 and start at ‘Factoring by Grouping’.

2. Rewrite   with four terms so that it can be factored by
grouping.

3. To factor we must find two numbers that multiply to
______ and that add to ______.

Use a table to find the two numbers.

Rewrite the trinomial with four terms so it can be factored.

Factor.

4. Factor showing all the steps as in .

6. List all the types of factoring you have learned so far in this chapter.
Give an example for each type.

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