Q 70E - Intermediate Algebra

Question

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

$m^2-13m+30$

Step-by-Step Solution

Answer

The factorization is $(m-3)(m-10)$.

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.