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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 7: Q 7.26. (page 816)

Factor: $- 7 a^{2} + 21 a$ .

Short Answer

Expert verified

The required factor is $- 7 a (a - 3)$ .

Step by step solution

01

Step 1. Given information.

The given polynomial is:

$- 7 a^{2} + 21 a$

02

Step 2. Find the GCF.

Find the GCF of $7 a^{2} and 21 a$ ,

$7 a^{2} = 7 \cdot a \cdot a 21 a = 3 \cdot 7 \cdot a$

GCF $= 7 a$

Since the leading coefficient is negative, the GCF is negative, $- 7 a$ .

03

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$- 7 a \cdot a - (- 7 a) \cdot 3$

Factor the GCF,

$- 7 a (a - 3)$

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Most popular questions from this chapter

In the following exercises, find the greatest common factor.

$42, 60$

Watermelon drop A springtime tradition at the University of California San Diego is the Watermelon Drop, where a watermelon is dropped from the seventh story of Urey Hall.

(a) The binomial $- 16 t^{2} + 80$ gives the height of the watermelon t seconds after it is dropped. Factor the greatest common factor from this binomial.

(b) If the watermelon is thrown down with initial velocity 8 feet per second, its height after t seconds is given by the trinomial $- 16 t^{2} - 8 t + 80 .$ Completely factor this trinomial.

Factor: $12 p + 12$

In the following exercises, factor completely.

$25 x^{2} + 35 x y + 49 y^{2}$

Find the Greatest Common Factor from a polynomial

$35 y + 84$

See all solutions

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