Question

(x-2) is a factor of the polynomial x^3 + 2ax^2+ax-8,find the value of a

Answer 1

The answer might be -10

Answer 2

$\textbf{ Hello Mate! }$

As given, ( x - 2 ) is factor of p(x) hence value of x = 2

$p(x) = {x}^{3} + 2a {x}^{2} + ax - 8$

As ( x - 2 ) is factor therefore p(2) = 0

$p(2) = {2}^{3} + 2a ({2}^{2} ) + a(2) - 8 \\ 0 = 8 + 8a + 2a - 8 \\ 0 = + 10a \\ 0 = a$

$\boxed{ Hence\:value\:of\:a\:is\:0 }$

Have great future ahead!