Q. 360 - Intermediate Algebra

Question

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

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

Step-by-Step Solution

Answer

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

Step 1. Given

The trinomial is $r^2+3rs-28s^2$

To find the factors of the trinomial.

Step 2. Write binomial with first term r and second term s

The binomial contains $r$ in the the first term and $s$ in the second term.

The last term of the trinomial is negative, so the factors must have opposite signs with greater number having positive sign.

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

Step 3. Find numbers multiply to - 28 and add to 3

Find the numbers multiply to $-28$ and add to $3$

Factors of $-28$	Sum of factors
$-1,28$	$27$
$-2,14$	$12$
$-4,7$	$3$

Step 4. Find the factors

Use $-4,7$ as coefficients of last term

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

Step 5. Check the answer

The factors are $(r-4s)(r+7s)$

Multiply the factors 

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

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

Hence the multiplication of factors gives the trinomial.