Question
2. Fill in the blanks to write the factored form of \( y^{2}+11 y+28 \). \( 2(y+\square)(y+\square) \)
Ask by Dickson Wang. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( y^{2} + 11y + 28 = (y + 4)(y + 7) \)
Solution
To factor the quadratic expression \( y^{2} + 11y + 28 \), we look for two numbers that multiply to **28** (the constant term) and add up to **11** (the coefficient of the middle term).
1. **Identify the numbers:**
- The numbers **4** and **7** satisfy these conditions because:
- \( 4 \times 7 = 28 \)
- \( 4 + 7 = 11 \)
2. **Write the factored form:**
- Using these numbers, the factored form of the quadratic is:
\[
(y + 4)(y + 7)
\]
**Note:** The expression does not require a leading coefficient of 2. Therefore, the correct factored form is:
\[
(y + 4)(y + 7)
\]
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Simplify this solution Bonus Knowledge
To factor the quadratic \( y^{2}+11 y+28 \), we look for two numbers that multiply to \( 28 \) and add up to \( 11 \). Those numbers are \( 7 \) and \( 4 \). Thus, the factored form is \( 2(y+7)(y+4) \). So, filling in the blanks, we get: \( 2(y+\mathbf{7})(y+\mathbf{4}) \).
