Question

(see example 1.)

1. $8v^2 + 8v - 48$
2. $6xy^2 - 24xy + 18x$
3. $9r^2s^3 - 36rs^4 - 45s^6$

polynomial. (see examples 2 and 3.)

1. $8m^2 + 30m + 7$
2. $10w^2 - 31w + 15$
3. $4z^2 + 4z - 3$
4. $18v^2 - 15v - 18$

he polynomial. (see example 4.)

1. $-7v^2 - 25v - 12$
2. $-8h^2 - 13h + 6$
3. $-22d^2 + 29d - 9$

Explanation:

Step1: Factor out GCF (Q2)

$8v^2 + 8v - 48 = 8(v^2 + v - 6)$

Step2: Factor quadratic (Q2)

$8(v^2 + v - 6) = 8(v+3)(v-2)$

Step3: Factor out GCF (Q4)

$6xy^2 - 24xy + 18x = 6x(y^2 - 4y + 3)$

Step4: Factor quadratic (Q4)

$6x(y^2 - 4y + 3) = 6x(y-1)(y-3)$

Step5: Factor out GCF (Q6)

$9r^2s^3 - 36rs^4 - 45s^6 = 9s^3(r^2 - 4rs - 5s^2)$

Step6: Factor quadratic (Q6)

$9s^3(r^2 - 4rs - 5s^2) = 9s^3(r-5s)(r+s)$

Step7: Factor quadratic (Q8)

$8m^2 + 30m + 7 = (4m+1)(2m+7)$

Step8: Factor quadratic (Q10)

$10w^2 - 31w + 15 = (5w-3)(2w-5)$

Step9: Factor quadratic (Q12)

$4z^2 + 4z - 3 = (2z+3)(2z-1)$

Step10: Factor out GCF then quadratic (Q14)

$18v^2 - 15v - 18 = 3(6v^2 - 5v - 6) = 3(3v+2)(2v-3)$

Step11: Factor out negative then quadratic (Q16)

$-7v^2 -25v -12 = -(7v^2 +25v +12) = -(7v+4)(v+3)$

Step12: Factor out negative then quadratic (Q18)

$-8h^2 -13h +6 = -(8h^2 +13h -6) = -(8h-3)(h+2)$

Step13: Factor out negative then quadratic (Q20)

$-22d^2 +29d -9 = -(22d^2 -29d +9) = -(11d-9)(2d-1)$

Answer:

1. $8(v+3)(v-2)$
2. $6x(y-1)(y-3)$
3. $9s^3(r-5s)(r+s)$
4. $(4m+1)(2m+7)$
5. $(5w-3)(2w-5)$
6. $(2z+3)(2z-1)$
7. $3(3v+2)(2v-3)$
8. $-(7v+4)(v+3)$
9. $-(8h-3)(h+2)$
10. $-(11d-9)(2d-1)$