Question

How do I factorise $10x - 15$?

Answer 1

Hint: In order to factorise the above linear expression in one variable, first write down the coefficient of x and the constant term in terms of their factors. After this look for the factors that are common in both, and take those factors to get your required result.

Complete step by step answer:
- We are given a linear expression in one variable $10x - 15$ and we have to factorise.
$ \Rightarrow 10x - 15$
- Since one term in the above is containing variable $x$ and another is a constant.
- So let’s try to write the coefficient of $x$ in term so its factor and similarly the constant value in its factors.
- We get, coefficient of $x$ i.e. $10$ can be written as $5 \times 2$ and the constant $15$ can be expressed as $5 \times 3$.
- Putting them into the expression, we get
$ \Rightarrow \left( {5 \times 2} \right)x - \left( {5 \times 3} \right)$
- As you can see we have $5$ is coming in both the term, so we can pull out $5$ and rewrite the expression as,
$ \Rightarrow 5(2x - 3)$
Hence, We have successfully factorised our expression.

Therefore, the factorisation of $10x - 15$ is $5(2x - 3)$.

Note: Linear Equation: A linear equation is an equation which can be represented in the form of $ax + c$ where $x$ is the unknown variable and a,c are the numbers known where $a \ne 0$. If $a = 0$ then the equation will become constant value and will no more be a linear equation. The degree of the variable in the linear equation is of the order 1. Every Linear equation has 1 root.