REMAINDER THEOREM

Question 1

What is the remainder when 3x2 - 5x + 6 is divided by x - 2 ?

Answer 1

remainder = p(2) x -2 =0
x =2
p(2) = 3x 2square -5x2 +6
= 12-10 +6 = 8

Question 2

-4 is a root of x4 + ax3 - 19x2 - 46x + 120

What is the value of a?

Answer 2

since -4 is a root (zero)  p(-4) =0
(-4)4 + a (-4)3  -19(-4)2 - 46(-4) +120 =0
 256 -64a - 304 +184 +120  =0
                      -64 a = -256
                            a = 4

Question 3

2 is a root of kx4 - 11x3 + kx2 + 13x + 2

What is the value of k?

Answer 3

since 2 is a root (zero)
           p(2) =0
     k (2)4 - 11(2)3 + k (2)2 + 13(2) +2 =0
 16k  -88 +4k +26 +2 = 0
                   20k = 60
                        k =3

Question 4

What is the remainder when 2x2 - 3x + 5 is divided by 2x - 1 ?

Answer 4

2x-1 =0 
  2x = 1
  x = 1/2
remainder = p(1/2)
p(1/2) =  2(1/2)2 -3(1/2) +5
          =  2x 1/4 -3/2 +5
           = 1/2 -3/2 +5
            = -1 +5 = 4