All right, let's factor the expression [tex]\( 6x^2 + x \)[/tex] completely. Here are the steps:
1. Identify the common factor:
- Look for the greatest common factor (GCF) in the terms [tex]\( 6x^2 \)[/tex] and [tex]\( x \)[/tex].
- Both terms contain the variable [tex]\( x \)[/tex].
2. Factor out the GCF:
- The GCF in this case is [tex]\( x \)[/tex].
- When factoring out [tex]\( x \)[/tex], we divide each term by [tex]\( x \)[/tex]:
[tex]\[
6x^2 \div x = 6x
\][/tex]
[tex]\[
x \div x = 1
\][/tex]
3. Write the factored form:
- After factoring out [tex]\( x \)[/tex], the given expression can be written as:
[tex]\[
x (6x + 1)
\][/tex]
Therefore, the completely factored form of the expression [tex]\( 6x^2 + x \)[/tex] is:
[tex]\[
x(6x + 1)
\][/tex]
