1. 3.6B Factoring Trinomials

2. Warm Up: Factor These Trinomials!
Factor each trinomial, if possible. The first four do NOT have leading coefficients, the last two DO have leading coefficients. Watch out for signs!!
x2 + 3x – 18
2x2 + x – 21
3) 3x2 + 11x + 10

3. Solution #4: x2 + 3x - 18 x2 + 3x - 18 = (x - 3)(x + 6)
1) Factors of -18:
1 • -18, -1 • 18
2 • -9, -2 • 9
3 • -6, -3 • 6
2) Which pair adds to 3 ?
3) Write the factors.
x2 + 3x - 18 = (x - 3)(x + 6)

4. Solution #5: 2x2 + x - 21 2x2 + x - 21 = (x - 3)(2x + 7)
1) Multiply 2 • (-21) = - 42; list factors of - 42.
1 • -42, -1 • 42
2 • -21, -2 • 21
3 • -14, -3 • 14
6 • -7, -6 • 7
2) Which pair adds to 1 ?
3) Write the temporary factors.
( x - 6)( x + 7) 2 2
4) Put “2” underneath. 3
( x - 6)( x + 7) 2
5) Reduce (if possible).
6) Move denominator(s)in front of “x”.
( x - 3)( 2x + 7)
2x2 + x - 21 = (x - 3)(2x + 7)

5. Concept: What Are Solutions?
The solution to a quadratic is the point (or points) where the parabola crosses the x–axis.
These are also sometimes called “roots,” “zero’s, or “x–intercepts.”
The solutions are –6 and 3.

6. Concept: How to Find the “zero’s”
Normally, in most classes this is what you have to learn in order to find the solutions:

7. Now would be a good time to start taking notes again. I’m just say’n.
Concept: How to Find the “zero’s”
Don’t freak out!!!!
Fortunately, Mrs. Davidson already taught you everything you need to find the solutions.
Remember when you learned to factor trinomials in section 3.5A?
The solutions were already there. You just need to know how to read them.
Now would be a good time to start taking notes again. I’m just say’n.

8. Concept: How to Find the “zero’s”
3x2 + 11x + 10
1) Multiply 3 • 10 = 30; list factors of 30.
1 • 30
2 • 15
3 • 10
5 • 6
2) Which pair adds to 11 ?
3) Write the temporary factors.
( x + 5)( x + 6) 3 3
4) Put “3” underneath. 2
( x + 5)( x + 6) 3
5) Reduce (if possible).
STOP!!! Your solutions are in front of you.
( x + 5)( x + 2) 3 5
x =
and x = 2 3