Question

The polynomials $(2x^3+x^2-ax+2)$ and $(2x^3-3x^2-3x+a)$ when divided by (x -2) leave the same remainder. Find the value of a.

Answer 1

$f\left(x\right)=2x^3+x^2-ax+2g\left(x\right)=2x^3-3x^2-3x+a\text{By remainder theorem, when f(x) is divided by x-2, then the remainder = f(2)}Putx=2inf\left(x\right),weget,f\left(2\right)=2(2{)}^3+(2{)}^2-a\left(2\right)+216+4-2a+2=-2a+22\text{By remainder theorem, when g(x) is divided by x-2, then the remainder = g(2)}Putx=2ing\left(x\right),weget,g\left(2\right)=2(2{)}^3-3(2{)}^2-3\left(2\right)+a16-12-6+a=-2+aItsisgiventhat,f\left(2\right)=g\left(2\right)-2a+22=-2+a-3a=-24a=8$

The value of a is 8