Question

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

$b^2+14b+48$

Short answer

The factors are$(b+6)(b+8)$.

Step-by-step solution

Step 1. Writing the expression

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

localid="1644544130598" $(b)(b)$.

Step 2. Finding the factors

We need to find two numbers whose product is $48$and sum is $14$.

Factors of$48$	Sum of factors
$1,48$	$49$
$2,24$	$26$
$3,16$	$19$
$4,12$	$16$
$6,8$	14

Thus $6,8$are the correct factors.

Thus, the factorization of the trinomiall is localid="1644542220674" $(b+6)(b+8)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (b+6)(b+8)=b^2+8b+6b+48 \\ (b+6)(b+8)=b^2+14b+48 \end{gathered}$$

Thus, the obtained factorization is correct.