Question

In the following exercises, factor each trinomial of the form $x^2+bxy+c{y}^2$

$r^2+3rs-28s^2$

Short answer

The factorization of$r^2+3rs-28s^2$is$(r+7s)(r-4s)$

Step-by-step solution

Step 1. Given information

Given expression is$r^2+3rs-28s^2$

Step 2. Find the last terms of the trinomials.

The factors of the expression:

Factors of -28	Sum of factors
7, -4	7 + (-4) = 3
14, -2	14 + (-2) = 12
28, -1	28 + (-1) = 27

Step 3. Factorization

Use $7$and $-4$as the last terms of the trinomials.

$r^2+3rs-28s^2=(r+7s)(r-4s)$

Step 4. Check

$$\begin{gathered} (r+7s)(r-4s)=r^2+7rs-4rs-28s^2 \\ =r^2+3rs-28s^2 \end{gathered}$$