Answer :
To factor the expression [tex]\(7x^3 + 28x^2\)[/tex], we can follow these steps:
1. Identify the greatest common factor (GCF):
The terms in the expression are [tex]\(7x^3\)[/tex] and [tex]\(28x^2\)[/tex]. The GCF of the coefficients, 7 and 28, is 7. Both terms also contain [tex]\(x\)[/tex] as a factor, with the smallest power being [tex]\(x^2\)[/tex].
2. Factor out the GCF:
We can factor out [tex]\(7x^2\)[/tex] from each term. The expression becomes:
[tex]\[
7x^2(x + 4)
\][/tex]
Here's how this works:
- [tex]\(7x^3\)[/tex] divided by [tex]\(7x^2\)[/tex] gives [tex]\(x\)[/tex].
- [tex]\(28x^2\)[/tex] divided by [tex]\(7x^2\)[/tex] gives 4.
3. Result:
So, the fully factored form of the expression [tex]\(7x^3 + 28x^2\)[/tex] is:
[tex]\[
7x^2(x + 4)
\][/tex]
This is the simplified, factored form of the given polynomial expression.
1. Identify the greatest common factor (GCF):
The terms in the expression are [tex]\(7x^3\)[/tex] and [tex]\(28x^2\)[/tex]. The GCF of the coefficients, 7 and 28, is 7. Both terms also contain [tex]\(x\)[/tex] as a factor, with the smallest power being [tex]\(x^2\)[/tex].
2. Factor out the GCF:
We can factor out [tex]\(7x^2\)[/tex] from each term. The expression becomes:
[tex]\[
7x^2(x + 4)
\][/tex]
Here's how this works:
- [tex]\(7x^3\)[/tex] divided by [tex]\(7x^2\)[/tex] gives [tex]\(x\)[/tex].
- [tex]\(28x^2\)[/tex] divided by [tex]\(7x^2\)[/tex] gives 4.
3. Result:
So, the fully factored form of the expression [tex]\(7x^3 + 28x^2\)[/tex] is:
[tex]\[
7x^2(x + 4)
\][/tex]
This is the simplified, factored form of the given polynomial expression.
