Lesson 30: Factoring Trinomials
A trinomial is a polynomial with three terms. Factoring trinomials is an important skill in algebra, especially when solving quadratic equations.
Factoring Trinomials of the Form ax² + bx + c
Steps:
- Identify a, b, and c in the trinomial ax² + bx + c.
- Find two numbers that multiply to a*c and add to b.
- Split the middle term using these two numbers.
- Factor by grouping.
Example 1:
Factor x² + 5x + 6
- a = 1, b = 5, c = 6
- Numbers that multiply to 6 and add to 5: 2 and 3
- Split middle term: x² + 2x + 3x + 6
- Group: (x² + 2x) + (3x + 6)
- Factor each group: x(x + 2) + 3(x + 2)
- Factor common binomial: (x + 2)(x + 3)
Example 2 (a ≠1):
Factor 2x² + 7x + 3
- a = 2, b = 7, c = 3
- Multiply a*c = 2*3 = 6 → Find two numbers that add to 7: 6 and 1
- Split middle term: 2x² + 6x + x + 3
- Group: (2x² + 6x) + (x + 3)
- Factor each group: 2x(x + 3) + 1(x + 3)
- Factor common binomial: (2x + 1)(x + 3)
Practice Problems
- Factor x² + 8x + 15
- Factor x² − 5x + 6
- Factor 3x² + 11x + 6
- Factor 4x² − 12x + 9