Question

Which of the following is the complete factorization of $9x^2?$

• A. $9\cdot x\cdot x$
• B. $3\cdot 3\cdot x^2$
• C. $3\cdot 3\cdot x\cdot x$
• D. None of the above

Answer 1

The correct option is C $3\cdot 3\cdot x\cdot x$

$\underset{–}{\text{Complete Factor of a Monomial}:}$
To factor a monomial completely, we write the coefficient as a product of primes and expand the variable part.

For example, to completely factor $15x^3,$ we can write the prime factorization of $15$ as $3\cdot 5$ and write $x^3$ as $x\cdot x\cdot x$. Therefore, the complete factorization of $15x^3$:$15x^3=3\cdot 5\cdot x\cdot x\cdot x$

$\underset{–}{\text{Need to Completely Factorize:}}9x^2$


Here, Coefficient: $9$ and
Variable part: $x^2$

Prime factorization of coefficient $9:$
$9=3\cdot 3$

Expension of variable part $x^2:$
$x^2=x\cdot x$

Therefore, complete factorization of $9x^2:$ $9x^2=3\cdot 3\cdot x\cdot x$

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