Determine whether the second polynomial is a factor of the first polynomial.
-$\left( 9 x ^ { 4 } + 19 x ^ { 3 } - 2 x ^ { 2 } + x + 4 \right) ; ( x + 2 )$
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if $ ( x + 2 ) $ is a factor of $ 9 x ^ { 4 } + 19 x ^ { 3 } - 2 x ^ { 2 } + x + 4 $, we can use the Remainder Theorem. According to the Remainder Theorem, if a polynomial $ f(x) $ is divided by $ (x - c) $, the remainder is $ f(c) $. Here, $ c = -2 $. Substituting $ -2 $ into the polynomial gives $ 9(-2)^4 + 19(-2)^3 - 2(-2)^2 + (-2) + 4 $, which simplifies to $ 144 - 152 + 8 - 2 + 4 $, not equal to zero. Therefore, $ ( x + 2 ) $ is not a factor of the given polynomial.

Determine Whether the Second Polynomial Is a Factor of the First