Question

Use Remainder Theorem to find the value of K , it being given that when $x^{3} + 2 x^{2} +k x + 3$ is divided by another polynomial ( $x - 3$ ), then the remainder is 21.

Answer 1

x-3)x³+2x²+kx+3(x²+5x+(k+15)
      (-)  (-)
      x³-3x²
      ----------
          5x² +  kx
          (-)       (-)
         5x²  -15x
              -----------
                (k+15)x+3
                   (-)         (-)
                (k+15)x-3(k+15)
          -         ---------------
                       3k+48          -remainder=21
3k+48=21
3k=(21-48)=-27
so k=-9

Answer 2

the answer to the following equation is -9