Question

Factor (x + 4)3 - 9x - 36 =
thank youuu :)

Answer 1

(x + 4)(x + 1)(x + 7)

Explanation:

(x + 4)³ - 9x - 36

(x + 4)³ - 9(x + 4)

(x + 4)[(x + 4)² - 9]

(x + 4)[(x + 4)² - 3²]

(x + 4)[(x + 4) - 3][(x + 4) + 3]

(x + 4)(x + 1)(x + 7)

Answer 2

`\left(x+1\right)\left(x+4\right)\left(x+7\right)`

Explanation:

First, let's simplify the given expression:

`(x + 4)^3 - 9x - 36 = 0` (Simplify the exponent)

=
`x^3 + 12x^2 + 48x + 64 - 9x - 36 = 0` (Combine like terms)

=
`x^3 + 12x^2 + 39x + 28 = 0` (According to the Rational Root Theorem, we can try to factor out 1 since it is a possible factor)

=
`\left(x+1\right)(x^3+12x^2+39x+28)/(x+1)` (Hey, it worked! Now we can simplify this)

=
`(x + 1)x^2+11x+28` (We can now factor x² + 11x + 28 as a regular quadratic trinomial)

=
`\left(x+1\right)\left(x+4\right)\left(x+7\right)`