Determine whether the second polynomial is a factor of the first polynomial.
-$\left( 5 x ^ { 3 } + 17 x ^ { 2 } - 11 x + 4 \right) ; ( x + 4 )$
A) Yes
B) No

Question

Quizplus · Accepted Answer

To determine if $ ( x + 4 ) $ is a factor of $ 5 x ^ { 3 } + 17 x ^ { 2 } - 11 x + 4 $, we can use the Remainder Theorem. According to the theorem, if $ p(x) $ is a polynomial and $ p(a) = 0 $ for some number $ a $, then $ (x - a) $ is a factor of $ p(x) $. Here, we substitute $ -4 $ into the polynomial: $ 5(-4)^3 + 17(-4)^2 - 11(-4) + 4 = 0 $. Since the result is 0, $ (x + 4) $ is indeed a factor of the given polynomial.

Determine Whether the Second Polynomial Is a Factor of the First