Question

When dividing x ^ 3 + n * x ^ 2 + 4nx - 6 by x + 3 the remainder is -48. What is the value of ?

Answer 1

The value of n is 5.

Solution:

Given equation:

$x^3+nx^2+4nx-6 \div x+3$

Remainder = -48

By remainder theorem,

x + 3 = 0

Add -3 on both sides.

x + 3 - 3 = 0 - 3

x = -3

Substitute x = -3 in given.

$\text{Remainder}=(-3)^{3}+n (-3)^{2}+4n(-3) -6$

$-48=-27+9n+-12n -6$

$-48=-33-3n$

Add 33 on both sides.

$-48+33=-33-3n+33$

$-15=-3n$

Divide by -3 on both sides.

$\frac{-15}{-3} =\frac{-3n}{-3}$

$5 = n$

The value of n is 5.