Question

for what value of a is(x-5) is factor of x^3-3a^2-10x+24

Answer 1

$x - 5 = 0 \\ x = 5 \\ substitute \: the \: value \: of \: x \: in \: this \: equation \: we \: get \\ 5 ^{3} - 3a ^{2} - 10(5) + 24 = 0 \\ 125 - 3a ^{2} - 50 + 24 = 0 \\ 99 - 3a ^{2} = 0 \\ 3a ^{2} = 99 \\ a ^{2} = 33 \\ a = \sqrt{33 \:} \: \: \: or \: \: \: - \sqrt{33}$