Question

If the factorization of the term $12x^2$ is $T\cdot 4x^2,$ then the value of $T$ is

Answer 1

$\underset{–}{\text{Factor of a Term}:}$
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.

$\underset{–}{\text{Given:}}$
Factorization of $12x^2$ is $T\cdot 4x^2$

$\underset{–}{\text{Need to Find}:}$ The value of $T$

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

$T\cdot 4x^2=12x^2$
Dividing by $4x^2$ on both side, we get

$\Rightarrow \frac{T\cdot 4x^2}{4x^2}=\frac{12x^2}{4x^2}$

$\Rightarrow T=\frac{3\times 4x^2}{4x^2}$

$\Rightarrow T=3$

Therefore, the required value of $T$ is $\underset{–}{3}.$