Learn it
To factor ax² + bx + c with a ≠ 1, find two numbers that multiply to a × c and add to b, then split the middle term and factor by grouping.
2x² + 7x + 3: a × c = 6; 6 and 1 add to 7. 2x² + 6x + x + 3 = 2x(x + 3) + 1(x + 3) = (2x + 1)(x + 3).
Special patterns: a² − b² = (a + b)(a − b); a² + 2ab + b² = (a + b)²; a² − 2ab + b² = (a − b)².
Worked examples
Example 1
Factor 3x² − 10x − 8.
- a × c = −24; numbers −12 and 2 (sum −10)
- 3x² − 12x + 2x − 8
- 3x(x − 4) + 2(x − 4)
Answer: (3x + 2)(x − 4)
Example 2
Factor 9x² − 25.
- Difference of squares: (3x)² − 5²
Answer: (3x + 5)(3x − 5)
Practice
Try these on paper first, then check your work.
- 2x² + 5x + 2
- 4x² − 49
- x² + 12x + 36
- 6x² + x − 2
Show the answer key
- (2x + 1)(x + 2)
- (2x + 7)(2x − 7)
- (x + 6)²
- (3x + 2)(2x − 1)