Question 29

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Jambmaths question: 

Find the expression $k{{x}^{3}}+{{x}^{2}}-5x-2$ leaves a remainder 2 when it is divided by 2x + 1

Option A: 

8

Option B: 

–10

Option C: 

10

Option D: 

–5

Jamb Maths Solution: 

Let $f(x)=k{{x}^{3}}+{{x}^{2}}-5x-2$ when 2x + 1is used to divide f(x), the remainder is 2,i.e. when x =– ½ and f(– ½) =2 $\begin{align}  & f(-\tfrac{1}{2})=k{{(-\tfrac{1}{2})}^{3}}+{{(-\tfrac{1}{2})}^{2}}-5(-\tfrac{1}{2})-2=2 \\ & =-\tfrac{1}{8}k+\tfrac{1}{4}+\tfrac{5}{2}-2=2 \\ & \frac{-k+2+20-16}{8}=2 \\ & -k+6=16 \\ & -k=10 \\ & k=-10 \\\end{align}$

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