What is the value of n in the expression x cubed -3x squared plus nx plus 5 when divided by x -3 leaves a remainder of 17?

Answer 1

By the remainder theorem, if the remainder, on division by (x - 3) is 17

then substituting x - 3 = 0 or, equivalently, x = 3 will give a value of 17 in the original expression.

Thus

33 - 3*32 + 3n + 5 = 17

So that 3n + 5 = 17

that is 3n = 12 or n = 4

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I do not see how this question can be answered when there are two unknown variables.

It is suggested above the answer is that n equals 4.

Let me substitute a random value for x.

x = 2

Would give:

(8 - 12 + 8 + 5) / (2 - 3)

= 9 / -1 = -9. There is no remainder. The remainder can not simultaneously be 0 and 17. There is an error here. (See below for why).

This question can not be answered when there are 2 unknowns.

Additional Information:-

The first answer is correct and the second answer given by another contributor is incorrect because by using the remainder theorem:-

f(x) = x3-3x2+nx+5 remainder 17

f(x) becomes f(3) because the divisor is x-3 and 3-3 = 0

f(3) = 33-3(3)2+3n+5 = 17

f(3) = 3n+5 = 17

f(3) = 3n = 17-5

f(3) = 3n = 12

f(3) = n = 4

So the value of n in the expression is 4 which makes the original answer correct.