Question

An irreducible factor of $24{\mathrm{x}}^2{\mathrm{y}}^2$ is:

• A. ${\mathrm{x}}^2$
• B. ${\mathrm{y}}^2$
• C. $\mathrm{x}$
• D. $24\mathrm{x}$

Answer 1

The correct option is C

$\mathrm{x}$

Step 1: Explanation of the correct option

An irreducible factor is a factor that cannot be expressed further as a product of factors. Such a factorization is called an irreducible factorization.

Factorization of $24{\mathrm{x}}^2{\mathrm{y}}^2=2\times 2\times 2\times 3\times \mathrm{x}\times \mathrm{x}\times \mathrm{y}\times \mathrm{y}$

It is clear that $\mathrm{x}$ cannot be expressed further as a product of factors. Hence $\mathrm{x}$ is an irreducible factor of $24{\mathrm{x}}^2{\mathrm{y}}^2$.

Therefore option (C) is correct.

Step 2: Explanation of the incorrect option

Option (A): ${\mathrm{x}}^2$ can be factorized as $\mathrm{x}\times \mathrm{x}$, therefore it is not an irreducible factor of $24{\mathrm{x}}^2{\mathrm{y}}^2$.

Option (B): ${\mathrm{y}}^2$ can be factorized as $\mathrm{y}\times \mathrm{y}$, therefore it is not an irreducible factor of $24{\mathrm{x}}^2{\mathrm{y}}^2$.

Option (D): $24\mathrm{x}$ can be factorized as $2\times 2\times 2\times 3\times \mathrm{x}$, therefore it is not an irreducible factor of $24{\mathrm{x}}^2{\mathrm{y}}^2$.

Therefore option (A), (B), and (D) do not give the correct answer.