What is the remainder when 3x4−4x2+8x−1 is divided by x−2 ?
Given, f(x)=3x4−4x2+8x−1.Here, f(x) is divided by (x−2).
Now, according to the remainder theorem, when f(x) is divided by (x−2), then the remainder is f(2). {∵x−2=0→x=2
Then,
f(2)=3(2)4−4(2)2+8(2)−1
=3(16)−4(4)+16−1
=48−16+16−1
=47.
Hence, the remainder obtained is 47.