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]
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]