Question

if x+2 is the factor ofx^4+ax^2+11x+6 find a​

Answer 1

Answer:

Let p(x) = x^4 +ax^2 +11x + 6

g(x) = x+2

By the factor thereom if g(x) is a factor of p(x) then p(-2) = 0

$p( - 2) = ( - 2) {}^{4} + a( - 2) {}^{2} + 11( - 2) + 6 \\ 16 + 4a - 22 + 6 = 0 \\ 4a = 28 \\ a = \frac{28}{4} \\ a = 7$