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Q2.

Expert-verifiedFound in: Page 33

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**To factor the trinomial** ${x}^{2}+7x+10$**, we look for two integers whose product is _____ and whose sum is _____. These integers are _____ and _____, so the trinomial factors as _______.**

To factor the trinomial ${x}^{2}+7x+10$, we look for two integers whose product is **10** and whose sum is **7**. These integers are **5 and 2** , so the trinomial factors as ${x}^{2}+7x+10=\left(x+5\right)\left(x+2\right)$

To factor a trinomial of the form $a{x}^{2}+bx+c$, we note that

$\left(x+r\right)\left(x+s\right)={x}^{2}+\left(r+s\right)x+rs$

So, we need to choose numbers r and s so that $r+s=b$ and $rs=c$.

Given ${x}^{2}+7x+10$

This is of the form $a{x}^{2}+bx+c$ where $b=7$ and $c=10$

The factorization of the trinomial will be $\left(x+r\right)\left(x+s\right)={x}^{2}+\left(r+s\right)x+rs$

So, we need to choose numbers r and s so that $r+s=b$ and $rs=c$.

We need to choose integers r and s so that $r+s=7$ and $rs=10$.

By trial and error we find that the two integers are $r=5,s=2$

$r+s=5+2=7$

$rs=5\cdot 2=10$

The factorization of the trinomial is

$\begin{array}{l}{x}^{2}+7x+10=\left(x+r\right)\left(x+s\right)\\ \Rightarrow {x}^{2}+7x+10=\left(x+5\right)\left(x+2\right)\end{array}$

**Complete the following table by stating whether the polynomial is a monomial, binomial, or trinomial; then list its terms and state its degree.**

Polynomial | Type | Term | Degree |

$-2{x}^{2}+5x-3$ |

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