Question

How to factor 3x³+3x²-36

Answer 1

Answer:

$3(x - 2) (x^2 + 3x + 6)$

Step-by-step explanation:

Firstly, divide all parts of the equation by 3:

$3x^3 + 3x^2-36$

$3(x^3 + x^2-12)$

Now focus on the equation:

$x^3 + x^2-12$

We know that the equation can be factored using x so we know that (x +- unknown) is the factor. We need to find the easiest way to factor this, lets find the factors of 12:

1 12

2 6

3 4

1 and 12 won't work so let's try 2 and 6, initially start as a negative 2:

$\frac{ x^3 + x^2 - 12}{x - 2}$ = $x^2 + 3x + 6$

We can confirm this is simplified by multiplying together:

$(x - 2) (x^2 + 3x + 6)$

$x* x^2 = x^3\\x * 3x = 3x^2\\x * 6 = 6x\\-2 * x^2 = -2x^2\\-2 * 3x = 6x\\-2 * 6 = -12$

= $x^3 + x^2 - 12$

Meaning it is simplified.

Now, put the equations together:

$3(x - 2) (x^2 + 3x + 6)$

Hope this helps!

Answer 2

Step-by-step explanation:

3x³+3x²-36

3(x³+ x²-12)

3(x - 2)(x²+3x +6)

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