Question

How do you factor completely $3x - 12$?

Answer 1

Hint: Here we have to factorize the linear equation. Factorization is defined as the process in which we break a number or a polynomial into a product of many factors of other polynomials, which when multiplied gives the original number. In the question we factorize the equation by taking $3$ as a common factor.

Complete step-by-step answer:
Factorization is defined as the process of expressing or decomposing a number or an algebraic expression as a product of its factors.
In the question we have to factorize the linear equation $3x - 12$. Linear equations are the equations in which we have a variable of maximum of one order in an equation.
So, we can factorize the equation $3x - 12$ by taking $3$ as a common factor.
Therefore,
$ \Rightarrow (3x - 12) = 3(x - 4)$
As we can see that if we multiply $3$ in $(x - 4)$ we get our original equation. i.e., $3x - 12$
Hence, $3(x - 4)$ is the factor of $3x - 12$.

Note: In factorization there is an important term ‘Factor’. Factor is defined as the numbers, algebraic variables or an algebraic expression which divides the number or an algebraic expression without leaving any remainder. For example- the factors of $42 = 2 \times 3 \times 7$, the numbers $2,3,7$ are the factors of $42$ and divide it without leaving any remainder. Similarly, for algebraic expression the factor of algebraic expression $6abc = 2 \times 3 \times a \times b \times c$.