Question

For what value of m is (x^3) - 2m(x)^2 +16 divisible by x+2 ??​

Answer 1

$\huge{\boxed{\texttt{Answer :-}}}$

♦ For solving this question we will use factor theorem .

>> Factor theorem :- In this theorem we substitute the value of x for which the equation becomes zero .

♦ Now as provided in question :-

$f(x) = x^3 - 2mx^2 + 16$

$g(x) = x + 2$

♦ As $g(x) = x + 2$ is a factor of

$f(x) = x^3 - 2mx^2 + 16$ then

$\implies x + 2 = 0$

$\implies x = -2$

♦ Now by substituting the value of $x = -2 \:in\: f(x)$

♦ Then

$f(-2) = (-2)^3 - 2m(-2)^2 + 16 = 0$

$\implies -8 -2m(4) + 16 = 0$

$\implies -8 -8m + 16 = 0$

$\implies -8m = -16 + 8$

$\implies -8m = -8$

$\implies m = \dfrac{-8}{-8}$

$\implies m = 1$

♦ So when the value of "m" is "1" then the $f(x) = x^3 - 2mx^2 + 16$ is divisible by $g(x) = x + 2$