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Q15.

Expert-verifiedFound in: Page 492

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 $\left(\mathbf{5}a-\mathbf{1}\right)\left(a-\mathbf{5}\right)$.

Combine like terms in the given polynomial.

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

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.

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

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

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 $\left(5a-1\right)\left(a-5\right)$.

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