If f, left bracket, x, right bracket, equals, 5, x, to the power 5 , plus, 3, x, cubed, plus, 2f(x)=5x

5
+3x
3
+2, then what is the remainder when f, left bracket, x, right bracketf(x) is divided by x, minus, 2x−2?

1 answer

To find the remainder when f(x)f(x) is divided by x−2x−2, we can use the remainder theorem. According to the remainder theorem, if f(a) is divided by (x−a), the remainder will be f(a).

In this case, we can plug in x=2x=2 into f(x)f(x) to find the remainder.

f(2) = 5(2)^5 + 3(2)^3 + 2f(2) = 5(32) + 3(8) + 2f(2)
Since we don't know the value of f(2), we cannot determine the exact value of the remainder.

Therefore, the remainder when f(x)f(x) is divided by x−2x−2 is 5(32) + 3(8) + 2f(2).