Question

Find the value of m for which x^3-22mx^2+16 is divisible by x+2

Answer 1

Answer:

$\because \: {x}^{3} - 22m {x}^{2} + 16 \: is \: divisible \: \\ by \: x + 2 \\ \therefore \: substituting \: x = - 2 \: in \: the \: \\ given \: expression \: we \: find: \\ ( - 2) ^{3} - 22m( { - 2})^{2} + 16 = 0 \\ - 8 + 88m + 16 = 0 \\ 88m + 8 = 0 \\ 8(11m + 1) = 0 \\ 11m + 1 = 0 \\11 m = - 1 \\ m \: = - \frac{1}{11}$