Use the factor theorem to decide whether or not the second polynomial is a factor of the first.
-$7 x ^ { 3 } + 18 x ^ { 2 } - 8 x + 3 ; x + 3$

Question

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The factor theorem states that a polynomial $f(x)$ is a factor of another polynomial $g(x)$ if and only if $f(c)=0$ when $x=c$. In this case, we can substitute $x=-3$ into the first polynomial to get:$$7 (-3)^3 + 18 (-3)^2 - 8 (-3) + 3 = -189 + 162 + 24 + 3 = 0$$Therefore, $x+3$ is a factor of $7 x ^ { 3 } + 18 x ^ { 2 } - 8 x + 3$.

Use the Factor Theorem to Decide Whether or Not the Second