Question

How do you factor $4{x^2} - 3x$?

Answer 1

Hint: Here we will find the factor of given expression by taking the common terms out from the expression. Before that we will discuss the definition of factorizations and some of the facts. Finally we get the required answer.

Complete step-by-step solution:
Factoring is the process of finding the factors and finding what to multiply together to get an expression. It is like “splitting” an expression into a multiplication of simpler expressions. Factoring is also the opposite of expanding.
We also need the highest common factor including any variables for finding factors.
With more experience factoring becomes easier.
If a given expression is not in standard form, rewrite it in standard form by putting the degrees in descending order.
This makes factoring easier and is sometimes even necessary to factor.
No matter how many terms a polynomial has, it is always important to check for a greatest common factor first.
If there is a GCF, it will make factoring the polynomial much easier because the number of factors of each term will be lower because we will have factored one or more of them out.
This is especially important if the GCF includes a variable.
If we forget to factor out this GCF, we may also forget to find a solution.
Here we have $4{x^2} - 3x$,
$x$ is common to each term.
So we can take this from the terms we get,
$ \Rightarrow x\left( {4x - 3} \right)$

Therefore, the given equation written as $x\left( {4x - 3} \right)$

Note: The factored form is usually best. When trying to factor, follow these steps:
“Factor out” any common terms
See if it fits any of the identities, plus any more you may know
Keep going till you can’t factor any more