Question
Factor the following trinomial. \[ x^{2}+8 x+15 \] Select the correct choice below and, if ne A. \( x^{2}+8 x+15=\square \) (Type your ans B. The polynomial is prime.
Ask by Chandler Pierce. in the United States
Mar 11,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The trinomial factors to \( (x+3)(x+5) \).
Solution
1. We start with the trinomial
\[
x^{2}+8 x+15.
\]
2. We look for two numbers that multiply to \(15\) (the constant term) and add up to \(8\) (the coefficient of \(x\)).
- The numbers \(3\) and \(5\) satisfy this:
\[
3 \times 5 = 15 \quad \text{and} \quad 3 + 5 = 8.
\]
3. Using these numbers, we can factor the trinomial as:
\[
x^{2}+8 x+15 = (x+3)(x+5).
\]
The correct choice is:
A. \( x^{2}+8 x+15=(x+3)(x+5) \).
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Simplify this solution The Deep Dive
To factor the trinomial \( x^{2}+8 x+15 \), we need to find two numbers that multiply to 15 (the constant term) and add up to 8 (the coefficient of the linear term). The numbers 3 and 5 fit the bill perfectly! Thus, we can express the trinomial as: \[ x^{2}+8 x+15=(x+3)(x+5) \] So, the factorization is \( (x+3)(x+5) \). Now you can easily solve for \( x \) by setting each factor to zero and finding the roots. Happy factoring!
