Factor -45x^3-60x^2-20x

− 5 ⋅ ( 3 +2 )^2

Step-by-step explanation:

−5x(3x+2)^2

Step-by-step explanation:

-45x^3-60x^2-20x

Factor out 5.

5(−9x^3-12x^2-4x)

Consider −9x^3-12x^2-4x. Factor out x.

x(−9x^2−12x−4)

Consider −9x^2−12x−4 Factor the expression by grouping. First, the expression needs to be rewritten as −9x^2+ax+bx−4. To find a and b, set up a system to be solved.

a+b=−12

ab=−9(−4)=36

Since ab is positive, a and b have the same sign. Since a+b is negative, a and b are both negative. List all such integer pairs that give product 36.

−1,−36

−2,−18

−3,−12

−4,−9

−6,−6

Calculate the sum for each pair.

−1−36=−37

−2−18=−20

−3−12=−15

−4−9=−13

−6−6=−12

The solution is the pair that gives sum −12.

a=−6

b=−6

Rewrite −9x^2−12x−4 as (−9x^2−6x)+(−6x−4).

(−9x^2−6x)+(−6x−4)

Factor out −3x in the first and −2 in the second group.

−3x(3x+2)−2(3x+2)

Factor out the common term 3x+2 by using distributive property.

(3x+2)(−3x−2)

Rewrite the complete factored expression.

5x(3x+2)(−3x−2)