Question

Which of these shows the following expression factored completely?
6x2 + 15x - 36

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

3(2x + 3)(x – 4)

(6x + 9(x – 4)

(2x - 3)(x + 4)

Answer 1

The complete factorization of the quadratic equation 6x² + 15x - 36 is given by:

$y = 6\left(x - \frac{1}{4}\right)(x + 4)$

How to factor a quadratic equation?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

Considering the roots $x_1$ and $x_2$, it can be factored as:

$y = a(x - x_1)(x - x_2)$

In this problem, the function is:

$y = 6x^2 + 15x - 36$

Hence the coefficients are $a = 6, b = 15, c = -36$, and:

$\Delta = b^2 - 4ac = 15^2 - 4(6)(-36) = 1089$

$x_1 = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-15 + \sqrt{1089}}{12} = \frac{1}{4}$

$x_2 = \frac{-b - \sqrt{\Delta}}{2a} = \frac{-15 - \sqrt{1089}}{12} = -4$

Hence:

$y = 6\left(x - \frac{1}{4}\right)(x + 4)$

More can be learned about quadratic equations at https://brainly.com/question/24737967

Answer 2

Answer:

The answer you're looking for is 3(2x-3)(x+4)