TRUE / FALSE. Is $ (x+4) $ a factor of $ f(x)=3 x^{4}-48 x^{2}+8 x+32 $ True False

Question

asked May 21, 2024 129k views

1 Answer

David Tew · Answer 1 · 2024-05-25T20:03:15+0000

Answer:

True

Explanation:

If
f(-4)=0 , then
(x+4) is a factor of the original polynomial by the Factor/Remainder Theorem:

$f(x)=3x^4-48x^2+8x+32\\f(-4)=3(-4)^4-48(-4)^2+8(-4)+32\\f(-4)=0$

Therefore,
(x+4) is a factor, meaning it is true.