Question

determine which of the following polynomials has (x+1) as a factor.x^4+2x^3+2x^2+x+1​

Answer 1

Here is your Answer

Here is your Answerhope it helps!!! :-D

Answer 2

To check whether g(x) is a factor of p(x),

we use factor theorem :

g(x) is a factor of p(x) if p(-1) = 0

$p(x) = {x}^{4} + 2x^{3} + 2x^{2} + x + 1 \\ p( - 1) = { - 1}^{4} + 2( - 1)^{3} + 2( - 1)^{2} + ( - 1) + 1 \\p( - 1) = 1 - 2 + 2 - 1 + 1 \\ p( - 1) = 1$

As p(-1) is not equal to 0, g(x) is not a factor of p(x).

Hope it helps!