Q. 359 - Intermediate Algebra

Question

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

$x^2+12xy+35y^2$

Step-by-Step Solution

Answer

The factors of the polynomial $x^2+12xy+35y^2$ is $(x+5y)(x+7y)$

Step 1. Given

The trinomial is $x^2+12xy+35y^2$

To find the factors of the trinomial.

Step 2. Write binomial with first term x and second term y

The binomial contains $x$ in the the each term and $y$ in the second term.

The last and second term of the binomial is positive, so the factors must have positive signs.

$x^2+12xy+35y^2=(x+\_y)(x+\_y)$

Step 3. Find numbers multiply to 35 and add to 12

Find the numbers multiply to $35$ and add to $12$.

Factors of $35$	Sum of factors
$1,35$	$36$
$5,7$	$12$

Step 4. Find the factors

Use $5,7$ as coefficients of last term

$x^2+12xy+35y^2=(x+5y)(x+7y)$

Step 5. Check the answer

The factors are $(x+5y)(x+7y)$

Multiply the factors 

$(x+5y)(x+7y)=x^2+7xy+5xy+35y^2$

                         $=x^2+12xy+35y^2$

Hence the multiplication of factors gives the trinomial.