Question

Using synthetic decision what is the factored form of this polynomial

x^3 + 3x^2 -13x -15

A, (x-2)(x-3)(x+3).
B,(x-1)(x-5)(x+3).
C, (x-3)(x+2)(x+3).
D, (x-3)(x+1)(x+5)

Answer 1

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

Explanation:

Given the set of answer choices, no synthetic division is required.

We know any rational roots will be from the set ±1, ±3, ±5, since these are the factors of -15. (This eliminates choices A and C.)

Of course, the product of the constants in the binomial factors will match the constant term in the given expression. (This eliminates choice B.)

So, before we start any synthetic division, we know the correct answer is D.