How do you use the factor theorem to determine whether x+3 is a factor of $-4x^3 + 5x^2 + 8$ ?

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Answer 1 · 2015-12-21T18:50:01

You evaluate this polynomial at $x = -3$ .

Let $P(X) = -4X^3 + 5X^2 + 8$ . If $X+3$ is a factor of $P$ , then $P(-3) = 0$ . Let's evaluate $P$ at $3$ .

$P(-3) = -4*(-3)^3 + 5*3^2 + 8 = 108 + 45 + 8 != 0$ so $X+3$ is not a factor of $P$ .

How do you use the factor theorem to determine whether x+3 is a factor of -4x^3 + 5x^2 + 8-4x^3 + 5x^2 + 8?