Question

How do you use the factor theorem to determine whether a-1 is a factor of `a^3 – 2a^2 + a – 2`?

Answer 1

`(a-1)` is not a factor of `a^3-2a^2+a-2`

Explanation:

According to factor theorem if `x-a` is a factor of polynomial function `f(x)`, then `f(a)=0`. Now let `(x-1)` be a factor of the function

`f(x)=a_0x^n+a_1x^(n-1)+a_2x^(n-2)+.......+a_n`

then `f(1)=a_0+a_1+a_2+.......+a_n=0`

This means that if `(a-1)` is a factor of polynomial function `a^3-2a^2+a-2`, then sum of its coefficients must be zero.

Here as `1-2+1-2=-2` and sum of coefficients is not zero,

`(a-1)` is not a factor of `a^3-2a^2+a-2`