Question

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

$a^2+25a+100$

Short answer

The factors are$(a+5)(a+20)$.

Step-by-step solution

Step 1. Writing the expression

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

localid="1644544102479" $(a)(a)$.

Step 2. Finding the factors

We need to find two numbers whose product is $100$and sum is $25$.

Factors of $100$	Sum of factors
$1,100$	$101$
$2,50$	$52$
$4,25$	$29$
$5,20$	$25$
$10,10$	$20$

Thus, $5,20$are the correct factors.

Hence, the factorization of the trinomial is$(a+5)(a+20)$.

Step 3. Check

Multiply the factorization to get the trinomial again.

$$\begin{gathered} (a+5)(a+20)=a^2+20a+5a+100 \\ (a+5)(a+20)=a^2+25a+100 \end{gathered}$$

Thus, the obtained factorization is correct.