Answer:
−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)
