Q. 362 - Intermediate Algebra

Question

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

$p^2-5pq-36q^2$

Step-by-Step Solution

Answer

The factors of the polynomial $p^2-5pq-36q^2$ is $(p+4q)(p-9q)$

Step 1. Given

The trinomial is $p^2-5pq-36q^2$

To find the factors of the trinomial.

Step 2. Write binomial with first term p and second term q

The binomial contains $p$ in the first term and $q$ in the second term.

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

$p^2-5pq-36q^2=(p+ q)(p- q)$

Step 3. Find numbers multiply to - 36 and add to - 5

Find the numbers multiply to $-36$ and add to $-5$.

Factors of $-36$	Sum of factors
$1,-36$	$-35$
$2,-18$	$-16$
$3,-12$	$-9$
$4,-9$	$-5$

Step 4. Find the factors

Use $4,-9$ as coefficients of last term

$p^2-5pq-36q^2=(p+4q)(p-9q)$

Step 5. Check the answer

The factors are $(p+4q)(p-9q)$

Multiply the factors 

$(p+4q)(p-9q)=p^2-9pq+4pq-36q^2$

                         $=p^2-5pq-36q^2$

Hence the multiplication of factors gives the trinomial.