Question

Find the missing factor $A$ that makes the following equality true.
$18x^5=\left(A\right)\left(6x\right)$

• A. $3x^5$
• B. $3x^4$
• C. $3x^3$
• D. $4x^3$

Answer 1

The correct option is B $3x^4$

$\underset{–}{\text{Factor of a Term}:}$
To factor a term means to express it as a product of two or more terms.

For example, below are several possible factorizations of $6x^4$.

• $6x^4=2x\cdot 3x^3$
• $6x^4=8x^2\cdot x^2$
• $6x^4=2x\cdot 2x\cdot 2x\cdot x$
• $6x^4=2\cdot 3\cdot x\cdot x\cdot x\cdot x$

$\underset{–}{\text{Note}:}$
Product of all the factors of a term is equal to the term itself.

$\underset{–}{\text{Given:}}$
$18x^5=\left(A\right)\left(6x\right)$

$\underset{–}{\text{Need to Find}:}$ The factor $A$

As we know, product of all the factors of a term is equal to the term itself.

$A\left(6x\right)=18x^5$
Dividing both sides by $6x$, we get

$\Rightarrow \frac{A\left(6x\right)}{6x}=\frac{18x^5}{6x}$

$\Rightarrow A=\frac{18}{6}{x}^{(5-1)}$ $(\because \frac{a^m}{a^n}=a^{(m-n)})$

$\Rightarrow A=3x^4$

Therefore, the required factor $A$ is $\underset{–}{3x^4}.$

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