select the correct answer.\nwhat is the completely factored form of this expression?\n$y^2 - 12y + 32$\na…

select the correct answer.\nwhat is the completely factored form of this expression?\n$y^2 - 12y + 32$\na. $(y + 4)(y + 8)$\nb. $(y - 4)(y - 8)$\nc. $(y + 18)(y + 2)$\nd. $(y - 18)(y - 2)$

select the correct answer.\nwhat is the completely factored form of this expression?\n$y^2 - 12y + 32$\na. $(y + 4)(y + 8)$\nb. $(y - 4)(y - 8)$\nc. $(y + 18)(y + 2)$\nd. $(y - 18)(y - 2)$

Answer

Explanation:

Step1: Find pair summing to -12, product 32

We need two numbers that add to $-12$ and multiply to $32$. These numbers are $-4$ and $-8$, since $(-4)+(-8)=-12$ and $(-4)\times(-8)=32$.

Step2: Factor the quadratic expression

Substitute the pair into the factored form of a quadratic $y^2+by+c=(y+m)(y+n)$, where $m$ and $n$ are the found numbers. $\boldsymbol{y^2 - 12y + 32=(y-4)(y-8)}$

Step3: Match with options

Compare the result to the given choices.

Answer:

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