How do you factor #24x^4+18x^3-27x^2#?

2 Answers
EZ as pi · Barney V.
Apr 26, 2017

#3x^2(4x-3)(2x+3)#

Explanation:

#24x^4+18x^3-27x^2#

Take out the common factor first:

#3x^2(8x^2+6x-9)#

Now find factors of the quadratic trinomial.

#:.3x^2(4x-3)(2x+3)#

Nghi N
Jun 23, 2017

f(x) = 3x^2(4x - 3)(2x + 3)

Explanation:

#f(x) = 3x^2 y = 3x^2(8x^2 + 6x - 9)#
Factor
#y = 8x^2 + 6x - 9 =# 8(x + p)(x + q)
Use the new AC Method to factor trinomial (Google Search)
Converted trinomial
#y' = x^2 + 6x - 72 =# (x + p')(x + q')
Find 2 numbers knowing sum (b = 6) and product (ac = - 72).
They are: p' = - 6 and q' = 12
Therefore: #p = (p')/a = -6/8 = - 3/4#, and #q = 12/8 = 3/2#
Factored form:
#y = 8(x - 3/4)(x + 3/2) = (4x - 3)(2x + 3)#
#f(x) = 3x^2y = 3x^2(4x - 3)(2x + 3)#

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