Question

Which shows one way to determine the factors of x3 + 5x2 – 6x – 30 by grouping?

x(x2 – 5) + 6(x2 – 5)
x(x2 + 5) – 6(x2 + 5)
x2(x – 5) + 6(x – 5)
x2(x + 5) – 6(x + 5)

Answer 1

x^3 + 5x^2 − 6x − 30 = (x^3 + 5x^2) + (−6x − 30)
= x^2(x + 5) − 6(x + 5)
= (x^2 − 6)(x + 5).

So the correct grouping is: x^2(x + 5) − 6(x + 5).