if the polynomial kx^3+3x^2-13 and q(x) = 2x^3-5x+k when divided by x-2.leaves the same remainder,find k..

Question

It is from polynomials

Answer 1

 

We can use synthetic division to find out the remainders in terms of k.

The remainder for the first polynomial is 8k-1 and for the second polynomial k+6 (see later).
So these remainders are the same and 8k-1=k+6; 7k=7 so k=1.

2 | k  3 ......... 0..... -13

.....k 2k ....6+4k  12+8k

.....k 3+2k 6+4k | -1+8k Rem: 8k-1

2 | 2 0 -5  k

.....2 4  8  6

.....2 4  3 | k+6 Rem: k+6

The remainder is 7 in each case.