Find the value of k if the division of the polynomial kx3 + 9x2 +4x – 10 by (x+3) leaves a
remainder( -22) .
Answers
Dividing x3-4x+p by x-3
we have, x-3|x3 -4x +p |x2 +3x+5
x3-3x2
- +
0 +3x2-4x
3x2-9x
- +
0+5x +p
5x -15
- +
0+p+15
The value of reminder being, (p+15) p≠15 otherwise [x2 +3x+5] would have been a factor of [x3-4x+p]
Given that if [Kx3 +4x2 +3x-4] if divided by (x-3) the reminder must be (p+15)
=> [(Kx3 +4x2 +3x-4)-(p+15)] = [Kx3 +4x2 +3x-p-19] = [(Kx3 +4x2 +3x -(p+19)] is completely divisible by (x-3)
Dividing [Kx3 +4x2 +3x-(p+1)] by (x-3)
x-3|Kx3 +4x2 +3x-(p+19) |Kx2 +(4+3K)x+(15+9K)
Kx3-3Kx2
- +
0+[4+3K]x2 +3x
[4+3K]x2-12x-9Kx
- + +
0 15x+9Kx-(p+19)
15x+9Kx -45-27K
- - + +
0 -p +26+27K