6x^3-9x^2-12x

Question

Factor completely and check mentally.

Answer 1

Given 6x^3-9x^2-12x

= x(6x^2-9x-12)

Now factorise 6x^2-9x-12.

Compare it to quadratic form ax^2+bx+c = 0

a = 6, b = -9, c = -12.

x = [-b±√(b^2-4ac)]/2a

x = [9±√(81+288)/12

x = [9±√369]/12

x = [9±19.20]/12

x = 28.20/12 and x = -10.20/12

x = 2.35 and x = -0.85

Factoring of given polynomial 6x^3-9x^2-12x = x(x-2.35)(x+0.85).

Check:

For x = 0 ⇒6(0)^3-9(0)^2-12(0) = 0

For x = 2.35 ⇒6(2.35)^3-9(2.35)^2-12(2.35)

= 77.86-49.70-28.2 = 0

For x  = -0.085 ⇒6(-0.85)^3-9(-0.85)^2-12(-0.85)

= -3.68-6.505+10.20 = 0.

Comments

correct answer.