QuestionAugust 25, 2025

Factor the polynomial, if possible 2s^2+11s+15 Select the correct choice below and fill in any answer boxes within your choice. A. 2s^2+11s+15=square (Type your answer in factored form.) B. The polynomial is prime.

Factor the polynomial, if possible 2s^2+11s+15 Select the correct choice below and fill in any answer boxes within your choice. A. 2s^2+11s+15=square (Type your answer in factored form.) B. The polynomial is prime.
Factor the polynomial, if possible 2s^2+11s+15 Select the correct choice below and fill in any answer boxes within your choice. A. 2s^2+11s+15=square (Type your answer in factored form.) B. The polynomial is prime.

Solution
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Answer

(s + 3)(2s + 5) Explanation 1. Identify the form The polynomial is quadratic in the form ax^2 + bx + c with a = 2, b = 11, and c = 15. 2. Find two numbers that multiply to ac and add to b Calculate ac = 2 \times 15 = 30. Find two numbers that multiply to 30 and add to 11. These numbers are 5 and 6. 3. Rewrite the middle term Rewrite 11s as 5s + 6s: 2s^2 + 5s + 6s + 15. 4. Factor by grouping Group terms: (2s^2 + 5s) + (6s + 15). Factor each group: s(2s + 5) + 3(2s + 5). 5. Factor out the common binomial Factor out (2s + 5): (s + 3)(2s + 5).

Explanation

1. Identify the form<br /> The polynomial is quadratic in the form $ax^2 + bx + c$ with $a = 2$, $b = 11$, and $c = 15$.<br />2. Find two numbers that multiply to $ac$ and add to $b$<br /> Calculate $ac = 2 \times 15 = 30$. Find two numbers that multiply to 30 and add to 11. These numbers are 5 and 6.<br />3. Rewrite the middle term<br /> Rewrite $11s$ as $5s + 6s$: $2s^2 + 5s + 6s + 15$.<br />4. Factor by grouping<br /> Group terms: $(2s^2 + 5s) + (6s + 15)$. Factor each group: $s(2s + 5) + 3(2s + 5)$.<br />5. Factor out the common binomial<br /> Factor out $(2s + 5)$: $(s + 3)(2s + 5)$.
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