Certainly! To factorize the expression [tex]\( 4x^2 + x^3 \)[/tex], let's follow these steps:
1. Write down the given expression:
[tex]\[
4x^2 + x^3
\][/tex]
2. Identify common factors:
Notice that both terms in the expression, [tex]\( 4x^2 \)[/tex] and [tex]\( x^3 \)[/tex], have a common factor of [tex]\( x^2 \)[/tex].
3. Factor out [tex]\( x^2 \)[/tex] from each term:
[tex]\[
4x^2 + x^3 = x^2(4 + x)
\][/tex]
Here, we divided each term by [tex]\( x^2 \)[/tex]:
- [tex]\( \frac{4x^2}{x^2} = 4 \)[/tex]
- [tex]\( \frac{x^3}{x^2} = x \)[/tex]
4. Reorder the expression inside the parentheses:
To conform to the standard polynomial form, which orders terms by descending powers of [tex]\( x \)[/tex], we rewrite the expression:
[tex]\[
x^2 (x + 4)
\][/tex]
So, the factorized form of [tex]\( 4x^2 + x^3 \)[/tex] is:
[tex]\[
x^2 (x + 4)
\][/tex]
This is the fully factorized form of the given expression.
