Question
Facturise the following Wise any method) 1. \( x^{2}+10 x+9 \)
Ask by Ray Elliott. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x^{2} + 10x + 9 = (x + 1)(x + 9) \)
Solution
To factorize the quadratic expression \( x^{2} + 10x + 9 \), you can use the **factoring by finding two numbers** that satisfy the following conditions:
1. **Multiply to the constant term** (\( c = 9 \)).
2. **Add up to the coefficient of the middle term** (\( b = 10 \)).
Let's apply this method step by step:
1. **Identify the coefficients:**
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = 10 \) (coefficient of \( x \))
- \( c = 9 \) (constant term)
2. **Find two numbers that multiply to \( c = 9 \) and add up to \( b = 10 \):**
- The numbers **1** and **9** satisfy these conditions because:
- \( 1 \times 9 = 9 \)
- \( 1 + 9 = 10 \)
3. **Write the factored form using these two numbers:**
\[
x^{2} + 10x + 9 = (x + 1)(x + 9)
\]
**Final Factored Form:**
\[
(x + 1)(x + 9)
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Extra Insights
To factor the quadratic expression \( x^{2}+10x+9 \), we look for two numbers that multiply to 9 (the constant term) and add up to 10 (the coefficient of \( x \)). The numbers 1 and 9 fit perfectly because \( 1 \times 9 = 9 \) and \( 1 + 9 = 10 \). Thus, we can rewrite the expression as: \( (x + 1)(x + 9) \). And there you have it, factored neatly! Need a shortcut for future problems? Remember the "Product and Sum" method! Just think of it as a treasure hunt - you're looking for two pals (numbers) that want to get together for a party (multiply to the constant) and also get along fabulously (add to the coefficient). It makes factoring a breeze!
