for what value of h iz d polynomial f(X)=2x^3-hx^2+5x+9 exactly divisible by (x+2) - Maths - Polynomials

Question

for what value of h iz d polynomial f(X)=2x^3-hx^2+5x+9 exactly
divisible by (x+2)

Ajanta Trivedi · Accepted Answer

the given polynomial is $f (x) = 2 x^{3} - h x^{2} + 5 x + 9$

if f(x) is exactly divisible by (x+2), put x+2=0 $\Rightarrow x = - 2$

therefore $f (- 2) = 0$

$2 * (- 2)^{3} - h * (- 2)^{2} + 5 * (- 2) + 9 = 0 - 16 - 4 h - 10 + 9 = 0 4 h = - 17 h = - \frac{17}{4}$

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