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Answer :
To factor the expression [tex]\(10x^3 + 25x^2\)[/tex], you can follow these steps:
1. Identify the greatest common factor (GCF):
- Look at the coefficients and terms of the expression. The terms are [tex]\(10x^3\)[/tex] and [tex]\(25x^2\)[/tex].
- The GCF of the coefficients 10 and 25 is 5.
- Both terms also have a factor of [tex]\(x^2\)[/tex].
2. Factor out the GCF from the terms:
- Factoring out [tex]\(5x^2\)[/tex] from [tex]\(10x^3\)[/tex] gives:
[tex]\[
\frac{10x^3}{5x^2} = 2x
\][/tex]
- Factoring out [tex]\(5x^2\)[/tex] from [tex]\(25x^2\)[/tex] gives:
[tex]\[
\frac{25x^2}{5x^2} = 5
\][/tex]
3. Write the expression as a product of the GCF and a binomial:
- Once you've factored out the GCF, the expression becomes:
[tex]\[
5x^2(2x + 5)
\][/tex]
Therefore, the factored form of the expression [tex]\(10x^3 + 25x^2\)[/tex] is [tex]\(5x^2(2x + 5)\)[/tex].
1. Identify the greatest common factor (GCF):
- Look at the coefficients and terms of the expression. The terms are [tex]\(10x^3\)[/tex] and [tex]\(25x^2\)[/tex].
- The GCF of the coefficients 10 and 25 is 5.
- Both terms also have a factor of [tex]\(x^2\)[/tex].
2. Factor out the GCF from the terms:
- Factoring out [tex]\(5x^2\)[/tex] from [tex]\(10x^3\)[/tex] gives:
[tex]\[
\frac{10x^3}{5x^2} = 2x
\][/tex]
- Factoring out [tex]\(5x^2\)[/tex] from [tex]\(25x^2\)[/tex] gives:
[tex]\[
\frac{25x^2}{5x^2} = 5
\][/tex]
3. Write the expression as a product of the GCF and a binomial:
- Once you've factored out the GCF, the expression becomes:
[tex]\[
5x^2(2x + 5)
\][/tex]
Therefore, the factored form of the expression [tex]\(10x^3 + 25x^2\)[/tex] is [tex]\(5x^2(2x + 5)\)[/tex].
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