y^2+12y+32

Answer 1

To factor the trinomial y^2 + 12y + 32, we need to find two numbers that multiply to 32 (the constant term) and add up to 12 (the coefficient of the middle term).

The two numbers are 8 and 4 because 8 * 4 = 32 and 8 + 4 = 12.

So, we can rewrite the trinomial as:

y^2 + 8y + 4y + 32

Now, we can factor by grouping:

y(y + 8) + 4(y + 8)

Factoring out the common factor from both terms, we get:

(y + 8)(y + 4)

Therefore, the factored form of y^2 + 12y + 32 is (y + 8)(y + 4).