Question

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

$m^2-13m+30$

Short answer

The factorization is$(m-3)(m-10)$.

Step-by-step solution

Step 1. Writing the expression

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

$(m)(m)$

Step 2. Finding the factors

We need to find two numbers whose product is $30$and sum is $-13$.

Factors of $30$	Sum of factors
$-1,-30$	$-31$
$-2,-15$	$-17$
$-3,-10$	$-13$
$-5,-6$	$-11$

Thus, $-3$and $-10$are the correct factors.

Hence, the factorization is$(m-3)(m-10)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (m-3)(m-10)=m^2-10m-3m+30 \\ (m-3)(m-10)=m^2-13m+30 \end{gathered}$$

Thus, the obtained factorization is correct.