To completely factor the polynomial [tex]\( 28x^3 - 4x \)[/tex], follow these steps:
1. Identify the common factor: Observe the terms in the polynomial [tex]\( 28x^3 \)[/tex] and [tex]\( 4x \)[/tex]. Notice that both terms have a common factor of [tex]\( 4x \)[/tex].
2. Factor out the common factor: Extract [tex]\( 4x \)[/tex] from each term:
[tex]\[
28x^3 - 4x = 4x (\frac{28x^3}{4x} - \frac{4x}{4x})
\][/tex]
3. Simplify the expression inside the parentheses: Compute the division for each term inside the parentheses:
- For the first term: [tex]\(\frac{28x^3}{4x} = 7x^2\)[/tex]
- For the second term: [tex]\(\frac{4x}{4x} = 1\)[/tex]
So, this simplification gives us:
[tex]\[
28x^3 - 4x = 4x (7x^2 - 1)
\][/tex]
4. Confirm the factoring: Verify that the expression is correct by distributing [tex]\( 4x \)[/tex] back through the parentheses:
[tex]\[
4x (7x^2 - 1) = 4x \cdot 7x^2 - 4x \cdot 1 = 28x^3 - 4x
\][/tex]
Thus, the complete factoring of the polynomial [tex]\( 28x^3 - 4x \)[/tex] is:
[tex]\[
\boxed{7x^2 - 1}
\][/tex]
Therefore, the given expression [tex]\( 28x^3 - 4x \)[/tex] can be factored as:
[tex]\[
28x^3 - 4x = 4x (7x^2 - 1)
\][/tex]
