Question

consider the roots of a cubic equation with integral coefficients: -1, -4, and 3. which choice is a factor of the cubic equation? a x + 3 b x - 1 c x - 4 d x - 3

Explanation:

Step1: Use the factor - root relationship

If \(r\) is a root of a polynomial equation \(P(x) = 0\), then \((x - r)\) is a factor of \(P(x)\).
Given the roots \(x=-1,x = - 4,x = 3\).
For a root \(x=a\), the corresponding factor is \((x - a)\).
When \(a=-1\), the factor is \((x+1)\); when \(a = - 4\), the factor is \((x + 4)\); when \(a = 3\), the factor is \((x - 3)\).

Answer:

D. \(x - 3\)