Question

Which of the following is the greatest common factor of the monomials
$8x^4,4x^3$ and $10x^2?$

• A. $x^3$
• B. $2x^3$
• C. $2x^2$
• D. None of the above

Answer 1

The correct option is C $2x^2$

$\underset{–}{\text{Given}:}$
Monomials: $8x^4,4x^3$ and $10x^2$

$\underset{–}{\text{Need to Find}:}$
Greatest common factor of given monomials, $8x^4,4x^3$ and $10x^2$

Firstly, let's factorize the given monomials indivisually:

$\bullet$ $8x^4=2\times 2\times 2\times x\times x\times x\times x$
$\bullet$ $4x^3=2\times 2\times x\times x\times x$
$\bullet$ $10x^2=2\times 5\times x\times x$

First, we can notice that the common factor is $2$ among all the term. Also, note that $x^2$ is factor of every term.

Hence, greatest common factor of given monomials is $2x^2.$

Therefore, option (c.) is the correct choice.