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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset 91影视 Explanations$ Math

2nd Edition 路 1240 pages

ISBN: 9780998625713

Chapter 7: Q 7.25. (page 816)

Factor: $- 4 b^{2} + 16 b$

Short Answer

Expert verified

The required factor is $- 4 b (b - 4)$ .

Step by step solution

01

Step 1. Given information.

The given polynomial is:

$- 4 b^{2} + 16 b$

02

Step 2. Find the GCF.

Find the GCF of $4 b^{2} and 16 b$ ,

$4 b^{2} = 2 路 2 路 b 路 b 16 b = 2 路 2 路 2 路 2 路 b$

GCF is:

localid="1647713925251" role="math" $= 2 路 2 路 b = 4 b$

Since the leading coefficient is negative, the GCF is negative,localid="1647713725349" $- 4 b$ .

03

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$- 4 b 路 b - (- 4 b) 路 4$

Factor the GCF,

$- 4 b (b - 4)$

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Most popular questions from this chapter

Factor by grouping

$x^{2} y 鈭� x y^{2} + 2 x 鈭� 2 y$

In the following exercises, find the greatest common factor.

$90, 150, 105$

Solve:

$b^{2} + 9 b + 14 = 0$

Of all the factoring methods covered in this chapter (GCF, grouping, undo FOIL, 鈥榓c鈥� method, special products) which is the easiest for you? Which is the hardest? Explain your answers.

Solve: $(3 m 鈭� 2) (2 m + 1) = 0 .$

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