What is the value of n in the expression x cubed plus nx squared plus 3x -5 when divided by x -2 with a remainder of -3 showing brief details of your work?

Answer 1

Use the remainder theorem:-

f(x) = x3+nx2+3x-5

f(x) becomes f(2) because the divisor is x-2 and 2-2 = 0

f(2) = 8+4n+6-5 = -3

f(2) = 4n+9 = -3

f(2) = 4n = -12

f(2) = n = -3

So the value of n in the expression is -3

Check: f(2) = 8+(4*-3)+6-5 = -3