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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 7.16. (page 813)

Factor: $3 y^{2} - 12 y + 27$

Short Answer

Expert verified

The required factor is $3 (y^{2} - 4 y + 9)$ .

Step by step solution

01

Step 1. Given information.

The given polynomial is:

$3 y^{2} - 12 y + 27$

02

Step 2. Find the GCF.

Find the GCF of $3 y^{2}, 12 y, and 27$ ,

$3 y^{2} = 3 \cdot y \cdot y 12 y = 2 \cdot 2 \cdot 3 \cdot y 27 = 3 \cdot 3 \cdot 3$

GCF $= 3$

03

Step 3. Find the factor.

Rewrite each term as a product using the GCF,

$3 \cdot y^{2} - 3 \cdot 4 y + 3 \cdot 9$

Factor the GCF,

$3 (y^{2} - 4 y + 9)$

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