Question

Find the HCF of $(x-2{)}^2$, $x^2-4$ and $x^2+x-6$.

• A. $y+2$
• B. $y+3$
• C. $y$
• D. $y^2+2y$

Answer 1

The correct option is C

$y$

Let, x = y+2

First expression: $(x-2{)}^2=((y+2)-2{)}^2=y^2$

Second expression: $x^2-4=\left(\right(y+2{)}^2-4)=y^2+4y$

Third expression: $x^2+x-6=(y+2{)}^2+x-6=y^2+5y$

$\therefore$ from the above expressions $y$ is the highest common factor.