Question

In the following exercises, factor each trinomial of the form$x^2+bx+c$ $a^2+25a+100$

Short answer

The factorization of $a^2+25a+100$is,$(a+20)(a+5)$.

Step-by-step solution

Step 1. Given information

Given expression is$a^2+25a+100$.

Step 2. Find the last terms of the binomials

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

$(a)(a)$

Find two numbers that multiply to $100$ and add to $25$.

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

Step 3. Factorization 

Use $20$and $5$as the last terms of the binomials.

$a^2+25a+100=(a+20)(a+5)$

Step 4. Check

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