Question

Check wether p(x)= x^3 - 5x^3+4x-3 is a factor of g(x)=x-2

Answer 1

If g(x)=x-a,
Then according to factor theorem, we can say that g(x) is a factor of p(x) when p(a)=0.

So, here our p(x) = x³-5x³+4x-3.
And g(x) = x-2.

So, if p(2) = 0 then g(x) is a factor of p(x).

p(2)=(2)³-5(2)³+4(2)-3.
=8-40+8-3.
=-27.

Since, p(2) ≠ 0, x-2 is not a factor of x³-5x³+4x-3.