Question

Which of the following is the complete factorization of $14x^3?$

• A. $2\cdot 7\cdot x\cdot x$
• B. $2\cdot 7\cdot x\cdot x^2$
• C. $2\cdot 7\cdot x\cdot x\cdot x$
• D. $14\cdot x\cdot x\cdot x$

Answer 1

The correct option is C $2\cdot 7\cdot x\cdot x\cdot x$

$\underset{–}{\text{Complete Factor of a Term}:}$
To factor a term 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 $15x^3$:$15x^3=3\cdot 5\cdot x\cdot x\cdot x$

$\underset{–}{\text{Need to Completely Factorize:}}14x^3$


Here, Coefficient: $14$ and
Variable part: $x^3$

Prime factorization of coefficient $14:$
$14=2\cdot 7$

Expension of variable part $x^3:$
$x^3=x\cdot x\cdot x$

Therefore, complete factorization of $14x^3:$ $14x^3=2\cdot 7\cdot x\cdot x\cdot x$

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