Answer :

Sure! Let's factor the expression [tex]\(20x^3 + 15x^2 - 50x\)[/tex] by taking out the greatest common factor (GCF).

### Step-by-Step Solution:

1. Identify the Greatest Common Factor (GCF):
- Look at the coefficients of each term: 20, 15, and -50.
- The GCF of 20, 15, and 50 is 5.
- Observe the variable terms: [tex]\(x^3\)[/tex], [tex]\(x^2\)[/tex], and [tex]\(x\)[/tex].
- The smallest power of [tex]\(x\)[/tex] present in each term is [tex]\(x\)[/tex].

2. Combine the GCF:
- The overall GCF of the entire expression is [tex]\(5x\)[/tex].

3. Factor Out the GCF:
- Divide each term in the expression by [tex]\(5x\)[/tex] and write the resulting expression inside parenthesis:

[tex]\[
20x^3 \div 5x = 4x^2
\][/tex]
[tex]\[
15x^2 \div 5x = 3x
\][/tex]
[tex]\[
-50x \div 5x = -10
\][/tex]

4. Write the Factored Expression:
- The expression [tex]\(20x^3 + 15x^2 - 50x\)[/tex] can be factored as:

[tex]\[
5x(4x^2 + 3x - 10)
\][/tex]

So, the factored form of the expression is [tex]\(5x(4x^2 + 3x - 10)\)[/tex].

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