Unit 4: Quadratic Expressions
Lesson 6: Factoring
[A]
ax 2  bx  c, a  1
Factoring Complex Quadratic Trinomials
Recall
( 2x + 3 ) ( x - 1 )
=
2x2 + x - 3
Any trinomial in the form ax2 + bx + c, where a ≠ 1 is called a
complex quadratic trinomial and can be factored in the following way:
1)
2)
3)
Determine what two integers have a product of ac and a sum of b
Break up the middle term of the trinomial using the two integers.
Common Factor by Grouping (2 terms at a time)
ex.
NOTE:
ex.
Factor 6m2 + 13m - 5.
Simple Quadratic Trinomials can also be in the form
ax2y2 + bxy + c OR ax2 + bxy + cy2
Factor 6m2 + 13mn – 5n2
ALTERNATIVE METHOD: (looping or “cross method”)
ex.
2m2 – 9m + 4
[B]
Examples
1.
Factor (completely), if possible.
a)
5y2 – 14y - 3
b)
9x2 – 15x - 4
c)
5r2s – 7rs + 2s
d)
8y2 + 12xy – 8x2
Note:


Always look for a common factor first when factoring.
Not all quadratic expression of the form
can be factored over integers.
ax 2  bx  c, a  1