Question

The following polynomial has factors:

P(x) = x3 + 3x2 - x - 3.

x - 1

x + 1

x - 3

Answer 1

(x-1)(x+1)(x+3)

Explanation:

first you group the 2 parts of the equation

{(x^3) + (3x^3)} {-x - 3}

you can take out x squared from the first group and are left with x+3 and you can take out -1 from the second group also leaving you with x+3. Because these groups match it means that x+3 is a factor.

x^2(x+3) -1(x+3)

combine them

(x^2-1) (x+3)

x squared minus one can be simplified more to (x-1) and (x+1) so the final answer is (x-1)(x+1)(x+3)