Question

Using remainder theorem find the remainder when 2 x minus 4 x square + 2 x + 5 is divided by x minus 3 and x + 2

Answer 1

f(x) = 2x³-4x²+2x+5                                            x-3=0

f(3) = 2*3³-4*3²+2*3+5                                       x=3

     =2*27-4*9+6+5

     =54-36+6+5

     =65-36

     =29

Again,

f(x) = 2x³-4x²+2x+5                                            x+2=0

f(-2) = 2*(-2)³-4*(-2)²+2*(-2)+5

      = 2*-8-4*4-4+5

      = -16-16-4+5

      = -36+5

      = -31

when we divide polynomial f(x)= 2x³-4x²+2x+5  by (x-3) we get reminder 29 and by (x+2) we get reminder -31 .