The value of n is 5.
Solution:
Given equation:
[tex]x^3+nx^2+4nx-6 \div x+3[/tex]
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.
[tex]\text{Remainder}=(-3)^{3}+n (-3)^{2}+4n(-3) -6[/tex]
[tex]-48=-27+9n+-12n -6[/tex]
[tex]-48=-33-3n[/tex]
Add 33 on both sides.
[tex]-48+33=-33-3n+33[/tex]
[tex]-15=-3n[/tex]
Divide by -3 on both sides.
[tex]$\frac{-15}{-3} =\frac{-3n}{-3}[/tex]
[tex]5 = n[/tex]
The value of n is 5.
