Use the Factor Theorem to determine whether the first polynomial is a factor of the second polynomial.
-$$x + 5 ; 3 x ^ { 3 } + 12 x ^ { 2 } - 14 x + 5$$
A) Yes
B) $\mathrm { No }$

Question

Quizplus · Accepted Answer

The Factor Theorem states that a polynomial $f(x)$ has a factor $x - c$ if and only if $f(c) = 0$. Here, we test if $x + 5$ is a factor of the given polynomial by evaluating the polynomial at $x = -5$. Substituting $x = -5$ into $3x^3 + 12x^2 - 14x + 5$ gives $3(-5)^3 + 12(-5)^2 - 14(-5) + 5 = -375 + 300 + 70 + 5 = 0$. Since the result is 0, $x + 5$ is indeed a factor of the polynomial.

Use the Factor Theorem to Determine Whether the First Polynomial x+5;3x3+12x2−14x+5x + 5 ; 3 x ^ { 3 } + 12 x ^ { 2 } - 14 x + 5x+5;3x3+12x2−14x+5

Use the Factor Theorem to Determine Whether the First Polynomial $x + 5 ; 3 x ^ { 3 } + 12 x ^ { 2 } - 14 x + 5$