Answer :

To factor the expression [tex]\(4x^2 + 28x^3\)[/tex], we follow these steps:

1. Identify Common Factors: Look at both terms, [tex]\(4x^2\)[/tex] and [tex]\(28x^3\)[/tex]. Notice that both terms have a common factor.

2. Determine the Greatest Common Factor (GCF):
- The coefficients are 4 and 28. The greatest common divisor of these numbers is 4.
- Both terms have the variable [tex]\(x\)[/tex] with the powers [tex]\(x^2\)[/tex] and [tex]\(x^3\)[/tex]. The lowest power of [tex]\(x\)[/tex] is [tex]\(x^2\)[/tex].

The GCF is therefore [tex]\(4x^2\)[/tex].

3. Factor Out the GCF:
- Divide each term by the GCF, [tex]\(4x^2\)[/tex].
- For the term [tex]\(4x^2\)[/tex], dividing by [tex]\(4x^2\)[/tex] gives us [tex]\(1\)[/tex].
- For the term [tex]\(28x^3\)[/tex], dividing by [tex]\(4x^2\)[/tex] leaves us with [tex]\(7x\)[/tex].

4. Write the Factored Form:
Combine the GCF outside a parenthesis with the results from dividing each term by the GCF inside. This gives us:

[tex]\[
4x^2(1 + 7x)
\][/tex]

This is the fully factored form of the expression [tex]\(4x^2 + 28x^3\)[/tex].

Other Questions