Given a function f(x) and a divisor
To Determine: the remainder when f(x) is divided by x+1
Solution:
Please note that when we divide a polynomial by f(x) by x-c, the remainder is f(c)
[tex]\begin{gathered} f(x)=x^4+8x^3+12x^2 \\ \text{divided by} \\ x+1 \end{gathered}[/tex]
equate x+1 to zero to get x
[tex]\begin{gathered} x+1=0 \\ x=-1 \end{gathered}[/tex]
If f(x) is divided by x+1, f(-1) is the remainder
Then
[tex]\begin{gathered} f(x)=x^4+8x^3+12x^2 \\ f(-1)=(-1)^4+8(-1)^3+12(-1)^2^{} \\ f(-1)=1+8(-1)+12(1) \\ f(-1)=1-8+12 \\ f(-1)=-7+12 \\ F(-1)=5 \end{gathered}[/tex]
Hence, the remainder, R = 5
