Question

When a polynomial 2x^3+3x^2+ax+b is divided by x-2 leaves remainder 2 and x+2 leaves r=-2 find a and b

Answer 1

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Answer 2

f(2)= 2(2)^3+3(2)^2+a(2)+b

2 =2(8)+3(4)+2a+b

2=16+12+2ab

2=28+2ab

2-28=2ab

-26=2ab

f(-2) =2(-2)+3(-2)+a(-2)+b

-2=2(-8)+3(-2)+(-2a+b)

-2 =-16+12-2ab

-2=-4-2ab

4-2=-2ab

2=-2ab

therefore,2ab-2ab=-26+2

2a and 2a are cancelled and b are 2 so 2b

then 2b=-24/2

b=-7

and (2).

-26=2a+b

-26=2a+12.( transposing 2a to LHS and -26 to RHS)

-2a=12-26

-2a=-14

a=-14/-2

a=-7

therefore a=-12 and b =-7

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