Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x^{2} + 13x + 36 = (x + 4)(x + 9) \)
Solution
To factor the quadratic expression \( x^{2} + 13x + 36 \), follow these steps:
1. **Identify the coefficients:**
- The quadratic is in the form \( ax^{2} + bx + c \), where:
- \( a = 1 \)
- \( b = 13 \)
- \( c = 36 \)
2. **Find two numbers that multiply to \( c \) (36) and add up to \( b \) (13):**
- List the pairs of factors of 36:
- \( 1 \times 36 = 36 \) and \( 1 + 36 = 37 \) (Not 13)
- \( 2 \times 18 = 36 \) and \( 2 + 18 = 20 \) (Not 13)
- \( 3 \times 12 = 36 \) and \( 3 + 12 = 15 \) (Not 13)
- \( 4 \times 9 = 36 \) and \( 4 + 9 = 13 \) (**This pair works**)
3. **Write the factored form:**
- Using the numbers 4 and 9, the quadratic can be factored as:
\[
x^{2} + 13x + 36 = (x + 4)(x + 9)
\]
**Final Answer:**
\[
x^{2} + 13x + 36 = (x + 4)(x + 9)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
To factor \( x^{2}+13x+36 \), we need to find two numbers that multiply to 36 and add up to 13. Those numbers are 9 and 4. So, we can write the expression as \( (x + 9)(x + 4) \). Now, you can quickly check your work by expanding \( (x + 9)(x + 4) \) back out to see if it matches the original expression. It's always a nice little reassurance!
