# How do you factor completely: #y² - 12y + 32#?

##### 2 Answers

#### Explanation:

because the middle sign is a minus

and the last sign is an addition, both the signs in the parenthesis would be minuses

now the two "

will be a pair of factors of

and add up to

so let's list the pairs of factors of

so it looks like the factor pair of

we would just substitute the two numbers in for the two "

and get

Solve f(y) = y^2 - 12y + 32

Ans: (y - 4)(y - 8)

#### Explanation:

Find 2 numbers p and q knowing sum (-12) and product (32).

p and q have same sign, since a and c same sign.

Factor pairs of 32 --> (2, 16)(4, 8). This sum is 12 = - b.

Then, p = -4 and q = -8 (their sum must be -12, and not 12)

f(y) = (y - 4)(y - 8)