College

Factor the trinomial:

[tex]20x^3 + 28x^2 + 60x[/tex]

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. [tex]20x^3 + 28x^2 + 60x = \square[/tex] (Factor completely.)

B. [tex]20x^3 + 28x^2 + 60x[/tex] is prime.

Answer :

To factor the trinomial [tex]\(20x^3 + 28x^2 + 60x\)[/tex], follow these steps:

1. Identify the Greatest Common Factor (GCF):
- Check the coefficients: 20, 28, and 60. The GCF of these numbers is 4.
- Each term also contains at least one [tex]\(x\)[/tex]. Therefore, the GCF for the entire expression is [tex]\(4x\)[/tex].

2. Factor out the GCF:
- Divide each term by the GCF [tex]\(4x\)[/tex]:
- [tex]\(20x^3\)[/tex] divided by [tex]\(4x\)[/tex] is [tex]\(5x^2\)[/tex].
- [tex]\(28x^2\)[/tex] divided by [tex]\(4x\)[/tex] is [tex]\(7x\)[/tex].
- [tex]\(60x\)[/tex] divided by [tex]\(4x\)[/tex] is [tex]\(15\)[/tex].

3. Write the factored form:
- Once you have divided each term by the GCF, the expression inside the parentheses is [tex]\(5x^2 + 7x + 15\)[/tex].

4. Express the final factored form:
- The trinomial factors into [tex]\(4x(5x^2 + 7x + 15)\)[/tex].

Thus, the factored form of the trinomial [tex]\(20x^3 + 28x^2 + 60x\)[/tex] is:
[tex]\[ 4x(5x^2 + 7x + 15) \][/tex]

Therefore, the correct choice is option A:
[tex]\[ 20x^3 + 28x^2 + 60x = 4x(5x^2 + 7x + 15) \][/tex]

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