Question

1. factor the expression completely.

-5y² - 10y + 15

1. factor the expression completely.

2y² + 2y - 24

1. factor the expression completely.

-4s² - 4s + 8

1. fully factor the expression.

-5x² - 22x - 8

1. fully factor the expression.

3r² - 14r + 8

1. fully factor the expression.

-18y² - 318y - 720

1. fully factor the expression.

-15r² - 147r + 624

1. factor the expression completely.

2x² - 14x + 24

Explanation:

Problem 1:

Step1: Factor out GCF -5

$-5(y^2 + 2y - 3)$

Step2: Factor quadratic trinomial

$-5(y+3)(y-1)$

Problem 2:

Step1: Factor out GCF 2

$2(y^2 + y - 12)$

Step2: Factor quadratic trinomial

$2(y+4)(y-3)$

Problem 3:

Step1: Factor out GCF -4

$-4(s^2 + s - 2)$

Step2: Factor quadratic trinomial

$-4(s+2)(s-1)$

Problem 4:

Step1: Factor out GCF -1

$-(5x^2 + 22x + 8)$

Step2: Factor quadratic trinomial

$-(5x+2)(x+4)$

Problem 5:

Step1: Split middle term

$3r^2 -12r -2r +8$

Step2: Factor by grouping

$3r(r-4)-2(r-4)=(3r-2)(r-4)$

Problem 6:

Step1: Factor out GCF -6

$-6(3y^2 + 53y + 120)$

Step2: Factor quadratic trinomial

$-6(3y+8)(y+15)$

Problem 7:

Step1: Factor out GCF -3

$-3(5r^2 + 49r - 208)$

Step2: Factor quadratic trinomial

$-3(5r+65)(r-4)=-3\cdot5(r+13)(r-4)=-15(r+13)(r-4)$

Problem 8:

Step1: Factor out GCF 2

$2(x^2 -7x +12)$

Step2: Factor quadratic trinomial

$2(x-3)(x-4)$

Answer:

1. $\boldsymbol{-5(y+3)(y-1)}$
2. $\boldsymbol{2(y+4)(y-3)}$
3. $\boldsymbol{-4(s+2)(s-1)}$
4. $\boldsymbol{-(5x+2)(x+4)}$
5. $\boldsymbol{(3r-2)(r-4)}$
6. $\boldsymbol{-6(3y+8)(y+15)}$
7. $\boldsymbol{-15(r+13)(r-4)}$
8. $\boldsymbol{2(x-3)(x-4)}$