Question

find a if x^3+x^2+ax+8 is divisible by x-1

Answer 1

$p(x) = {x}^{3} + {x}^{2} + ax + 8 \\ x - 1 \: is \: \: divisible \: by \: p(x) \\ \\ p(1) = 0 \\ {(1)}^{3} + {(1)}^{2} + a(1) + 8 = 0 \\ 1 + 1 + a + 8 = 0 \\ 10 + a = 0 \\ a = - 10$