Question

Use the remainder theorem to find the remainder when f(x) is divided by x-1. Then use the factor theorem to determine whether x-1 is a factor of f(x).

f(x)=4x⁴-9x³+14x-9

The remainder is ____

Is x-1 a factor of f(x)=4x⁴-9x³+14x-9?

Yes or No

Answer 1

Given: is to be divided by (x-1)

According to remainder theorem, the remainder of f(x) divided by (x-a) is f(a).

f(a) is obtained by replacing all x terms in f(x) by "a".

If f(a)=0, then according to remainder theorem (x-a) is a factor of f(x).

Since f(1)=0, we can conclude that (x-1) is a factor of f(x) by remainder theorem.

Using factor theorem:

We can verify if (x-1) is a factor of f(x) if on synthetic division of is zero.

Verification is attached in the picture attached.

The remainder of synthetic division of f(x) by (x-1) is 0. So, using factor theorem, we can conclude that (x-1) is a factor of f(x).

The remainder of f(x) divided by (x-a) is zero.

Yes (x-a) is a factor of