Chapter 7: Q 115. (page 833)

In the following exercises, factor each expression.
$x^{2} - 14 x - 32$

Short Answer

Expert verified

The factorization of $x^{2} - 14 x - 32$ is, $(x + 2) (x - 16)$ .

Step by step solution

Step 1. Given information

Given expression is $x^{2} - 14 x - 32$ .

Step 2. Find the last terms of the binomials

Write the factors as two binomials with the first terms $x$ .

$(x) (x)$

Find two numbers that multiply to $- 32$ and add to $- 16$ .

Factors of -32	Sum of factors
-1, 32	-1 + 32 = 31
-2, 16	-2 + 16 = 14
-4, 8	-4 + 8 = 4
-8, 4	-8 + 4 = -4
-16, 2	-16 + 2 = -14*
-32, 1	-32 + 1 = -31

Step 3. Factorization

Use $2$ and $- 16$ as the last terms of the binomials.

$x^{2} - 14 x - 32 = (x + 2) (x - 16)$

Step 4. Check

$(x + 2) (x - 6) = x^{2} + 2 x - 16 x - 32 = x^{2} - 14 x - 32$

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In the following exercises, factor each expression.
$x^{2} - 14 x - 32$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the binomials

Step 3. Factorization

Step 4. Check

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In the following exercises, factor each expression.x2-14x-32

Short Answer

Step by step solution

Step 1. Given information

Step 2. Find the last terms of the binomials

Step 3. Factorization

Step 4. Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Geometry

Discrete Mathematics

Probability and Statistics

Pure Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, factor each expression.
$x^{2} - 14 x - 32$