Question

select the correct answer.
what is the completely factored form of this expression?
y² - 12y + 32
a. (y + 4)(y + 8)
b. (y - 4)(y - 8)
c. (y + 18)(y + 2)
d. (y - 18)(y - 2)

Explanation:

Step1: Find two numbers

We need two numbers that multiply to \(32\) and add up to \(-12\) (since the middle term is \(-12y\) and the constant term is \(32\)). The numbers are \(-4\) and \(-8\) because \((-4)\times(-8) = 32\) and \((-4)+(-8)=-12\).

Step2: Factor the quadratic

Using the numbers found, we can factor the quadratic \(y^{2}-12y + 32\) as \((y - 4)(y - 8)\).

Answer:

B. \((y - 4)(y - 8)\)