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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 7.18. (page 814)

Factor: $6 y^{3} - 15 y^{2}$ .

Short Answer

Expert verified

The required factor is $3 y^{2} (2 y - 5)$ .

Step by step solution

01

Step 1. Given information.

The given polynomial is:

$6 y^{3} - 15 y^{2}$

02

Step 2. Find the GCF.

Find the GCF of $6 y^{3} and 15 y^{2}$ ,

$6 y^{3} = 2 \cdot 3 \cdot y \cdot y \cdot y 15 y^{2} = 3 \cdot 5 \cdot y \cdot y$

GCF is:

$= 3 \cdot y \cdot y = 3 y^{2}$

03

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$3 y^{2} \cdot 2 y - 3 y^{2} \cdot 5$

Factor the GCF,

$3 y^{2} (2 y - 5)$

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Most popular questions from this chapter

Factor by grouping

$5 x - 5 y - y + x$

Factor: $- 16 z - 64$ .

Factor Differences of Squares

In the following exercises, factor.

$20 x^{2} - 125$

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.

In the following exercises, factor completely.

$3 v^{4} - 768$

See all solutions

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