When the polynomialf(x) = −3x^3 + kx^2 + lx − 8 is divided by x − 2 then the remainder is -28 and when it is divided by x + 1 then the remainder is 5. Find the values of k and l.

Answer 1

use synthetic division

-1 |-3 k l -8 |

3 -k-3 k+3-l-8=5

k-l=10

k=10 + l

2 |-3 k l -8 |

2l+4k-24 -8 =-28

2l+4k=4

2l +40+4l =4

6l = -36

l= -6

k = 4

f(x)=-3x^3+4x^2-6x-8