Question

Which shows one way to determine the factors of x^3+5x^2-6x-30 by grouping?

Answer 1

The factors of this equation are x = sqrt(6), x = -sqrt(6) and x = -5.

In order to find these by grouping, we start by just taking the first two terms. We then pull out the greatest common factor.

x^2 + 5x^2

x^2(x + 5)

Now we do the same for the last two.

-6x - 30

-6(x + 5)

Since the two parenthesis left behind are exactly the same, we can use them along with the factors pulled out, multiplied together.

(x^2 - 6)(x + 5)

Now to find the factors, we simply set both parenthesis separately equal to 0.

x + 5 = 0

x = -5

x^2 - 6 = 0

x^2 = 6

x = +/-sqrt(6)