# Factoring Polynomials

12 Problems. Please see the attached file for the fully formatted problems.

Section 4.1

Find the greatest common factor for each of the following sets of terms.

Exercise 14

, ,

Exercise 42

Factor each of the following polynomials.

Exercise 60

Find the GCF of each product.

Exercise 62

The area of a rectangle of length x is given by Find the width of the rectangle.

Section 4.2

Factor each of the following trinomials completely.

Exercise 56

Exercise 66

Find all positive values for k for which each of the following can be factored.

Section 4.3

Factor each of the following polynomials completely.

Exercise 52

Exercise 70

Section 4.4

Factor the following binomials

Exercise 28

Exercise 48

Determine whether each of the following trinomials is a perfect square. If it is, factor the trinomial.

Exercise 60

Factor each expression.

Exercise 64

Find a value for k so that will have the factors 3m + 7n and 3m - 7n.

Section 4.5

Factor each polynomial by grouping the first two terms and the last two terms.

Exercise 8

Exercise 16

Factor each polynomial completely by factoring out any common factors and then factor by grouping. Do not combine like terms.

Section 4.6

Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored.

Exercise 22

Exercise 24

Exercise 68

Exercise 100

Section 4.7

Factor each polynomial completely. To begin, state which method should be applied as the first step, given the guidelines of this section. Then continue the exercise and factor each polynomial completely.

Exercise 8

Exercise 28

Exercise 32

Factor completely.

Section 4.8

Solve each of the following quadratic equations.

Exercise 24

Exercise 48

If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm . What were the dimensions of the original square?

#### Solution Summary

Polynomials are factored.