2.1.5b Factoring ax2 + bx + c
Essential Question:
How do you factor complex trinomials?
Factoring More Trinomials
• Today, we are factoring trinomials when x2 has
the coefficient a.
• You can still use the same methods, but be
careful! You need to look for patterns that
incorporate a, b, and c.
Methods for Factoring
• Extended X Factor Method
ac (product)
b (sum)
1) Multiply a and c for the top
number
2) Use X Factor
3) Put A, two B’s, and C into Punnett
Square
4) Take out the GCF of each row and
column
5) Simplify answer
Methods for Factoring
• Sometimes, numbers are too large or difficult
to think of a combination using the extended
X factor method, so using reverse FOIL to just
guess and check until you have the desired
amounts.
Ex. 1 Factoring ax2 + bx + c
Ex. 1 Practice
Ex. 2 Factoring when c is Positive
Ex. 3 Practice
Special Cases
1) Perfect Square Trinomial: identical factors.
–
Example: 4x2 - 12x + 9 = (2x – 3)(2x – 3) = (2x – 3)2
2) Difference of Two Squares: Opposite factors
–
Example: 9x2 – 25 = (3x + 5)(3x – 5)
3) Not Factorable: cannot be factored (no
combination works)
–
Example: 2x2 + 3x + 25
Factoring out a GCF
•
What if the numbers are too big? AHHH, panic! No, just take out a GCF, then factor.
• If the numbers are too big in the trinomial, factor out
a GCF, then factor.
• Example: 20x2 + 80x + 35
Factoring out a GCF
•
What if the numbers are too big? AHHH, panic! No, just take out a GCF, then factor.
• If the numbers are too big in the trinomial, factor out
a GCF, then factor.
• Practice: 4y2 + 14y + 6
Summary
• Answer the essential question in detailed,
complete sentences.
• How do you factor complex trinomials?
• Write 3-5 study questions in the left column
to correspond with the notes.