Question

Find the value of ‘k’ if (x + 2) is a factor p(x) = x3 + 8x2 – kx – 2 ans fast I will make branlist​

Answer 1

       $\underline{\bold{Solution:}}$

       $\text{It is given that }(x+2) \text{ is a factor of }p(x) = x^{3} + 8x^{2} - kx - 2$

       $\text{Applying the factor theorem}$

$\implies p(-2) = 0$

$\implies p(-2) = (-2)^{3}+8(-2)^{2} - k(-2) - 2 = 0$

       $\text{Simplifying...}$

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

       $\text{Simplifying...}$

$\implies -8 +32 +2k - 2 = 0$

       $\text{Simplifying...}$

$\implies 22 + 2k = 0$

       $\text{Transposing }2k \text{ to R.H.S}$

$\implies22 = -2k$

       $\text{Transposing }2 \text{ to R.H.S}$

$\implies \dfrac{22}{-2} = k$

       $\text{Simplifying...}$

$\implies \boxed{-11=k}$