Question

Find the remainder when x^3+3x^2+5x+6x is divided by
1) x-2
2) x+2
3) x-3
4) x+3
5) x-4​

Answer 1

Answer:

Let, f(x) = x^3+3x^2+5x+6

f(2) = 2^3+3*2^2+5*2+6

= 8+12+10+6

= 36

f(-2) = (-2)^3+3(-2)^2+5(-2)+6

= -8+12-10+6

= 0

f(3) = 3^3+3(3)^2+5*3+6

= 27+27+15+6

= 75

f(-3) = (-3)^3+3(-3)^2+5(-3)+6

= -27+27-15+6

= -9

f(4) = 4^3+3(4)^2+5*4+6

= 64+48+20+6

= 138

The remainder are 36, 0, 75, -9, 138.