How to Factor Polynomials With Simple Examples
How to Factor Polynomials With Simple Examples
Factoring polynomials means breaking a polynomial into simpler expressions that multiply together to form the original expression. It is a key concept in algebra used for solving equations and simplifying expressions.
Basic Idea
For quadratic expressions like x² + bx + c, we try to find two numbers that:
- Multiply to give c
- Add to give b
Example 1
Factor: x² + 5x + 6
- Numbers: 2 and 3
- 2 × 3 = 6 and 2 + 3 = 5
Answer: (x + 2)(x + 3)
Example 2
Factor: x² + 7x + 10
- Numbers: 2 and 5
- 2 × 5 = 10 and 2 + 5 = 7
Answer: (x + 2)(x + 5)
Example 3
Factor: x² + 9x + 20
- Numbers: 4 and 5
- 4 × 5 = 20 and 4 + 5 = 9
Answer: (x + 4)(x + 5)
Example 4
Factor: x² + 11x + 24
- Numbers: 3 and 8
- 3 × 8 = 24 and 3 + 8 = 11
Answer: (x + 3)(x + 8)
Example 5
Factor: x² + 13x + 36
- Numbers: 4 and 9
- 4 × 9 = 36 and 4 + 9 = 13
Answer: (x + 4)(x + 9)
Example 6
Factor: x² + 14x + 49
- Numbers: 7 and 7
- 7 × 7 = 49 and 7 + 7 = 14
Answer: (x + 7)(x + 7)
Example 7
Factor: x² + 6x + 8
- Numbers: 2 and 4
- 2 × 4 = 8 and 2 + 4 = 6
Answer: (x + 2)(x + 4)
Conclusion
Factoring polynomials becomes easy when you practice finding number pairs that match multiplication and addition conditions. With time, you can solve these quickly without extra steps.