1. End Warm Up Answer each question to solve x2 – 9x + 18 = 0
Determine the values of a, b and c.
Factor the quadratic expression using what you know about b and c.
(x )(x ) = 0
Set each factor to zero and solve.
10 minutes
End

2. Answer (x-6)(x-3) = 0 Solutions: 6 and 3
Answer each question to solve x2 – 9x + 18 = 0
Determine the values of a, b and c.
Factor the quadratic expression using what you know about b and c.
(x )(x ) = 0
Set each factor to zero and solve.
(x-6)(x-3) = 0
Solutions: 6 and 3

3. Solving Quadratics By Factoring (a≠1)

4. What happens when a≠1?
On Friday, we found a relationship between two binomials and their product in standard form:
ax2 + bx + c
In each of our examples, a = 1. When a ≠ 1, we first want to see if there is a GCF we can factor out.

5. Example 1: Factor 3x2 – 27x + 54

6. Example 2: Solve 3x2 + x – 10 = 0

7. Example 3: Solve 4x2 + 4x – 3 = 0
Remember: Look for GCF, factor by trial and error, then set each factor to 0.
Answers: ½, -3/2

8. Example 4: Solve 10x2 - 18x – 24 = 0
Factor out 2 first! Answers: -4/5, 3

9. Example 5: Solve 4x2 + 3x = 0
Factor out x first! Answers: 0, -3/4

10. Homework
Complete the worksheet

11. Factoring when a ≠ 1 and no common factor
When a ≠ 1 and there is no common factor, factoring involves and trial and error process.
Factor 3x2 + x – 10
We can’t start with (x )(x ) like before because that won’t give us 3x2. What two values will multiply to 3x2?
(3x )(x )
Because c is negative, we need a negative factor and a positive factor. What two numbers will multiply to -10?
Plug in your numbers and check them by distributing. If it doesn’t work, try switching the signs or using different factors.

12. Solving by Factoring when a ≠ 1
Will our solutions just be the opposite of our factors like before?
Solve 3x2 + x – 10 = 0
We just factored this into (3x – 5)(x + 2) = 0.
Does x = 5 work?
(3(5) – 5)(5 + 2) = (10)(7) ≠ 0 NO!
We must SOLVE each factor by setting it equal to 0.
3x – 5 = 0 x + 2 = 0
x = 5/3 x = -2