Factoring Trinomials: $ax^2 + bx + c$
Factor trinomials of the form ax²+bx+c in Grade 9 algebra. Use the AC method to find factor pairs, split the middle term, and factor by grouping into two binomials.
Key Concepts
New Concept When a trinomial takes the form $ax^2 + bx + c$, the pattern [for factoring $x^2+bx+c$] no longer works. A new pattern emerges. What’s next Next, you’ll learn the systematic process of testing factor pairs to break down these more complex trinomials into simpler binomials.
Common Questions
How do you factor a trinomial ax² + bx + c?
Multiply a × c, find two numbers that multiply to ac and add to b, split the middle term using those numbers, then factor by grouping to get two binomial factors.
What is the AC method for factoring trinomials?
The AC method multiplies the leading coefficient a by constant c, finds factor pairs of ac that sum to b, rewrites the middle term, then factors by grouping.
How do you check if your trinomial factoring is correct?
Multiply your two binomial factors using FOIL. If the result matches the original trinomial ax² + bx + c, your factoring is correct.