Question

Find the HCF of the following pair of polynomials:
$x^2-2x+1$ and $x^2-3x+2$.

Answer 1

We know that $HCF$ is the highest common factor.

Factorise $x^2-2x+1$ as follows:

$x^2-2x+1=x^2-x-x+1=x(x-1)-1(x-1)=(x-1)(x-1)$

Now, factorise $x^2-3x+2$ as follows:

$x^2-3x+2=x^2-2x-x+2=x(x-2)-1(x-2)=(x-1)(x-2)$

Since the common factor between the polynomials $x^2-2x+1$ and $x^2-3x+2$ is $(x-1)$.

Hence, the $HCF$ is $(x-1)$.