Q 68E - Intermediate Algebra

Question

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

$q^2-13q+36$

Step-by-Step Solution

Answer

The factorization is $(q-4)(q-9)$.

Step 1. Writing the expression

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

$(q )(q )$.

Step 2. Finding the factors

We need to find two numbers whose product is $36$ and sum is $-13$.

Factors of $36$	Sum of factors
$-1, -36$	$-37$
$-2, -18$	$-20$
$-3, -12$	$-15$
$-4, -9$	$-13$
$-6, -6$	$-12$

Thus, $-4$ and $-9$ are the correct factors.

Hence, the factorization is $(q-4)(q-9)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (q-4)(q-9)=q^2-9q-4q+36 \\ (q-4)(q-9)=q^2-13q+36 \end{gathered}$$

Thus, the obtained factorization is correct.