Question
Factor the trinomial completely. \( 5 x^{2}+10 x-240 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( 5 x^{2}+10 x-240=\square \) (Factor completely.) B. The polynomial is prime.
Ask by Mejia Adkins. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( 5x^2 + 10x - 240 = 5(x + 8)(x - 6) \)
Solution
1. Factor out the greatest common factor (GCF) from all terms. The GCF is \(5\):
\[
5x^2 + 10x - 240 = 5(x^2 + 2x - 48)
\]
2. Factor the quadratic \(x^2 + 2x - 48\) by finding two numbers that multiply to \(-48\) and add to \(2\). These numbers are \(8\) and \(-6\) because:
\[
8 \times (-6) = -48 \quad \text{and} \quad 8 + (-6) = 2
\]
3. Write the factorization of the quadratic:
\[
x^2 + 2x - 48 = (x + 8)(x - 6)
\]
4. Substitute back the factor of \(5\):
\[
5x^2 + 10x - 240 = 5(x + 8)(x - 6)
\]
Thus, the correct choice is:
A. \( 5x^2+10x-240 = 5(x+8)(x-6) \).
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Extra Insights
To factor the trinomial \( 5x^{2} + 10x - 240 \), we can start by factoring out the greatest common factor (GCF), which is 5: \[ 5(x^{2} + 2x - 48) \] Now we need to factor the quadratic \( x^{2} + 2x - 48 \). We are looking for two numbers that multiply to -48 and add up to 2. These numbers are 8 and -6. Therefore, we can write it as: \[ 5(x + 8)(x - 6) \] So, the complete factorization of the original trinomial is: A. \( 5x^{2}+10x-240=5(x + 8)(x - 6) \)
