Question

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

Answer 1

`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)`

Answer 2

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)`