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Expert-verified Found in: Page 492 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # Factor each polynomial.$\mathbf{5}{a}^{2}-\mathbf{25}a-a+\mathbf{5}$

The factors of given polynomial are $\left(\mathbf{5}a-\mathbf{1}\right)\left(a-\mathbf{5}\right)$.

See the step by step solution

## Step 1. Combine.

Combine like terms in the given polynomial.

$5{a}^{2}-26a+5$

## Step 2. Find the GCF.

Find the GCF of $5{a}^{2},26a$ and 5.

$5{a}^{2}=1\cdot 5\cdot a\cdot a\phantom{\rule{0ex}{0ex}}26a=1\cdot 2\cdot 13\cdot a\phantom{\rule{0ex}{0ex}}5=1\cdot 5$

Therefore, GCF is 1.

## Step 3. Apply factoring pattern of ax2+bx+c.

There are two numbers having product of 25 and sum of $-26$. The numbers are $-1$ and $-25$.

$5{a}^{2}+mx+nx+5=5{a}^{2}-25a-1a+5$

## Step 4. Group terms with common factors and factor out GCF.

Group terms with common factors and factor out GCF from each grouping.

$\left(5{a}^{2}-25a\right)+\left(-1a+5\right)=5a\left(a-5\right)-1\left(a-5\right)\phantom{\rule{0ex}{0ex}}=\left(5a-1\right)\left(a-5\right)$

Therefore, the factors of $5{a}^{2}-25a-a+5$ are $\left(5a-1\right)\left(a-5\right)$. ### Want to see more solutions like these? 