Question

Match the expressions on the left side with their HCF given on the right side.

• A. $x+3$
• B. $x-2$
• C. $x-3$
• D. $x^2{y}^2$

Answer 1

Let us factorize the given expressions.

$x^2-9=x^2-3^2=(x+3)(x-3)$

$(x+3{)}^2=(x+3\left)\right(x+3)$

So, their HCF is $(x+3)$.

$x^2+x-6=(x+3)(x-2)$

$x^2-4=(x+2)(x-2)$

So, their HCF is $(x-2)$.

Now, $x^2+x-12=(x-3)(x+4)$
So, HCF of $x^2+x-12$ and $x-3$ is $(x-3)$.

In the expressions $x^2{y}^3$ and $x^3{y}^2{z}^7$,
Lowest power of $x$ is $x^2$.
Lowest power of $y$ is $y^2$.
Lowest power of $z$ is $z^0$

$\therefore$ H.C.F. = $x^2{y}^2$