Factoring Trinomials: $x^2 + bx + c$
Factor trinomials of the form x²+bx+c in Grade 9 algebra by finding two numbers that multiply to c and add to b, then writing them as factors (x+p)(x+q) in Saxon Algebra 1.
Key Concepts
New Concept This procedure can be reversed to factor a trinomial into the product of two binomials. What’s next Next, you'll apply this pattern to factor trinomials by examining the signs of their terms and finding the correct factor pairs.
Common Questions
What is the method for factoring x² + bx + c?
Find two integers p and q such that p × q = c and p + q = b. Then write the factored form as (x + p)(x + q). For x² + 5x + 6: need numbers multiplying to 6 and adding to 5 → 2 and 3 → (x+2)(x+3).
How do you factor a trinomial with a negative constant, like x² - x - 12?
Find numbers multiplying to -12 and adding to -1. Options: 3 × (-4) = -12 and 3 + (-4) = -1 ✓. Factored form: (x + 3)(x - 4). With negative constants, one factor must be positive and one negative.
How do you verify a trinomial factoring is correct?
Expand the factored form using FOIL. For (x+3)(x-4): x² - 4x + 3x - 12 = x² - x - 12. If this matches the original trinomial, the factoring is correct.