Question

Is x+a a factor of 4x^4+2x^3-3x^2+8x +109

Answer 1

f(x) = x + 2

p(x) = 4x^4 + 2x^3 - 3x^2 + 8x - 20 ....(2)

To check if f(x) is a factor of p(x), we need to divide them.

x + 2 = 0

x = (-2) ....(1)

Putting (1) in (2):

\begin{gathered}4 {( - 2)}^{4} + 2 {( - 2)}^{3} - 3 {( - 2)}^{2} + 8( -2) - 20 \\ \\ = > 64 - 16 - 12 - 16 - 20 \\ \\ = > 0\end{gathered}

4(−2)

4

+2(−2)

3

−3(−2)

2

+8(−2)−20

=>64−16−12−16−20

=>0

THEREFORE, f(x) is a factor of p(x).

HOPE IT HELP ☺️