Question

How do you factor \[8x - 4\]?

Answer 1

Hint: Here in this question, we have to find the factors for the given equation. The given equation is in the form of an algebraic equation. The equation has a degree one. By taking the common terms we can determine the factors. hence we obtain the required solution for the question.

Complete step-by-step solution:
The equation is in the form of an algebraic equation, where the algebraic equation is a combination of constants and variables. In algebraic equations or expressions we have three different kinds and they are monomial, binomial and polynomial.
Now consider the given equation \[8x - 4\]. This is an algebraic equation, containing the variable as x. The equation is of the form of a binomial algebraic equation.
In the given question we have two numerals 8 and 4.
Let we factorise these numerals we have

therefore the numeral 8 can be written as \[8 = 2 \times 2 \times 2\]

therefore the numeral 4 can be written as \[4 = 2 \times 2\]
so now the given equation is written as
\[ \Rightarrow 8x - 4 = (2 \times 2 \times 2)x - (2 \times 2)\]
let we take \[(2 \times 2)\] as common from both terms we have
\[ \Rightarrow 8x - 4 = (2 \times 2)\left( {2x - 1} \right)\]
on simplifying we have
\[ \Rightarrow 8x - 4 = 4\left( {2x - 1} \right)\]
hence we have obtained the factors for the given equation.
Therefore 4 and (2x – 1) are the factors of (8x – 4)

Note: This equation has degree one there is no specified formula like the quadratic equation. To determine the factors we have to factorise the terms involved in the equation and then take the common terms from the equation, they are the factors of the equation. Hence the tables of multiplication are important to solve these kinds of problems.