Question

Use polynomial division to completely factor y=x^3+3x^2-13x-15 by x+5

Answer 1

(x - 3)(x + 1)(x + 5)

Explanation:

I'd use synthetic division instead. If we were to find the roots of the given polynomial, we could from them write the factors as well.

The divisor x + 5 corresponds to root x = -5. Setting up synthetic div.,

-5 ) 1 3 -13 -15

-5 10 +15

-----------------------------

1 -2 -3 0

Since the remainder is 0, we know that -5 is a root and (x + 5) is a factor. Moreover, we know that the coefficients of the quotient are 1, -2 and -3.

1x² - 2x - 3 can be factored: the factors are (x - 3) and (x + 1).

So the end result for this problem is (x - 3)(x + 1)(x + 5).