Question

How do you factor \[5x-4\]?

Answer 1

Hint: This type of problem is based on the concept of factoring a polynomial. First, we have to consider the polynomial with degree 1. First, we have to look for any common term which can be a variable or constant. Since, there is no variable common, we can take a constant. Try taking any number common out of the bracket and see if they can be considered as a factor.

Complete step by step solution:
According to the question, we are asked to find the factors of \[5x-4\].
We have been given the polynomial is \[5x-4\]. ---------(1)
The given polynomial is of degree 1 and variable x.
To find the factors, we have to find the common term which can be a variable or constant.
Here, we find that x is only in the first term of the polynomial. Thus, we cannot take x common.
We have to look for a constant.
 Let us take -1 common from polynomials (1).
\[\Rightarrow 5x-4=-1\left( -5x+4 \right)\]
On further simplification, we get
\[5x-4=-\left( 4-5x \right)\]
But still we get the same polynomial and there is no factor.
Now, let us take 5 common from the polynomial.
\[\Rightarrow 5x-4=5\left( x-\dfrac{4}{5} \right)\]
Since we cannot consider a constant as a factor, this is also not the factor of the polynomial.
Let us now take 4 common from the polynomial.
\[\Rightarrow 5x-4=4\left( \dfrac{5x}{4}-1 \right)\]
In this case also, we cannot find any factors.
We can try for any constants and the result is the same.
Therefore, there are no factors for the polynomial 5x-4.

Note: Whenever we get such a type of problem, we should always find the degree of the polynomial. We cannot find factors for polynomials with degree 1. Also a constant cannot be considered as the factor of a polynomial. Only a term with a variable can be considered as a factor.