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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 6: Q. 6.10 (page 569)

Factor: $- 7 a^{3} + 21 a^{2} - 14 a$

Short Answer

Expert verified

The factored form is $\begin{array}{rcl} - 7 a (a^{2} - 3 a + 2) \end{array}$ .

Step by step solution

01

Step 1. Given Information

The given expression is $- 7 a^{3} + 21 a^{2} - 14 a$ .

02

Step 2. Rewrite the given expression

Express each of the term of the given expression as a product of GCF, $- 7 a$ .

$- 7 a 路 a^{2} - (- 7 a) 路 3 a + (- 7 a) 路 2$

Use the reverse distributive property, $a b + a c = a (b + c)$ to rewrite the obtained expression.

role="math" localid="1644852717553" $- 7 a 路 a^{2} - (- 7 a) 路 3 a + (- 7 a) 路 2 = - 7 a (a^{2} - 3 a + 2)$

03

Steck 3. Check

Multiply the obtained factors.

$\begin{array}{rcl} - 7 a (a^{2} - 3 a + 2) & = & - 7 a 路 a^{2} - (- 7 a) 路 3 a + (- 7 a) 路 2 \\ = & - 7 a^{3} + 21 a^{2} - 14 a \end{array}$

Since the obtained expression is the same as the given expression, the obtained factors are verified.

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