Question

if p(x)=x³-5x²+4x-3 and g(x)=x-2,show that g(x) is not a factor of p(x).

Answer 1

here we can see that if x-2 will be a factor of the p(x) then it would divide the p(x) which means that g(x)=0 or x=2
and when we substitute x=2 in the given equation we did not get the value of p(x) as zero hence it is not a factor of p(x)

Answer 2

I think you would be knowing the fact that if a number is factor of another number then it means it (factor) divides the number completly
i.e. the remainder is zero and if it is not a factor then remainder won't be zero.
It is same in case of a polynomial too.
If g(x) is not a factor of p(x) then it means remainder will not be zero.
When you'll divide x³-5x²+4x-3 by x -2 you will get -7 as remainder, which is not equal to zero.
Hence, g(x) is not a factor of p(x)