Question

question 9
factor the following problem completely. first factor out the greatest common factor, and then factor the remaining trinomial.
10y² + 90y + 180
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question 10
factor the following problem completely. first factor out the greatest common factor, and then factor the remaining trinomial.
5y² - 10y - 40
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Explanation:

(Question 9):

Step1: Factor out GCF

The greatest common factor of $10y^2$, $90y$, and $180$ is $10$.
$10y^2 + 90y + 180 = 10(y^2 + 9y + 18)$

Step2: Factor the trinomial

Find two numbers that multiply to $18$ and add to $9$ (these numbers are $6$ and $3$).
$y^2 + 9y + 18 = (y + 6)(y + 3)$

Step3: Combine factors

Substitute the factored trinomial back into the expression.
$10(y + 6)(y + 3)$

(Question 10):

Step1: Factor out GCF

The greatest common factor of $5y^2$, $-10y$, and $-40$ is $5$.
$5y^2 - 10y - 40 = 5(y^2 - 2y - 8)$

Step2: Factor the trinomial

Find two numbers that multiply to $-8$ and add to $-2$ (these numbers are $-4$ and $2$).
$y^2 - 2y - 8 = (y - 4)(y + 2)$

Step3: Combine factors

Substitute the factored trinomial back into the expression.
$5(y - 4)(y + 2)$

Answer:

Question 9: $10(y + 6)(y + 3)$
Question 10: $5(y - 4)(y + 2)$