Question

In the following exercises, factor each trinomial of the form $x^2-bx+c$.

$5p-6+p^2$

Short answer

The factorization is$(p+6)(p-1)$.

Step-by-step solution

Step 1. Rearranging terms

Rearrange the terms from highest to lowest degree.

We get,

$p^2+5p-6$

Step 2. Writing the expression

Write the factors as two binomials with first terms $p$.

$(p)(p)$

Step 3. Finding the factors

We need to find two numbers whose product is $-6$and sum is $5$.

Since the last term is negative, the coefficients will have opposite signs.

Factors of$-6$	Sum of factors
$-2,3$	$1$
$6,-1$	$5$

Thus, $6$and $-1$are the correct factors.

Hence, the factorization is$(p+6)(p-1)$.

Step 4. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (p+6)(p-1)=p^2-p+6p-6 \\ (p+6)(p-1)=p^2+5p-6 \end{gathered}$$

Thus, the obtained factorization is correct.