Question

If f, of, x, equals, 2, x, to the power 4 , plus, 3, x, squared, minus, 3f(x)=2x
4
+3x
2
−3, then what is the remainder when f, of, xf(x) is divided by x, minus, 1x−1?

Answer 1

If f(x) = 2x^4 + 3x^2 − 3, then the remainder of f(x f(x)) upon division by x − 1 is f(1·f(1)) = f(f(1)). Compute f(1) = 2(1)^4 + 3(1)^2 − 3 = 2. Then f(2) = 2(2^4) + 3(2^2) − 3 = 32 + 12 − 3 = 41.

So the remainder is 41.