1. 5.2: Solving Quadratic Equations by Factoring
(p. 256)
How do you factor:
x2 +bx +c
ax2+bx+c
a2 −b2
a2 +2ab +b2
a2 −2ab +b2
How do you solve a quadratic function?
Everything you ever learned about factoring in one section!

2. To solve a quadratic eqn
To solve a quadratic eqn. by factoring, you must remember your factoring patterns!

3. Zero Product Property
Let A and B be real numbers or algebraic expressions. If AB=0, then A=0 or B=0.
This means that If the product of 2 factors is zero, then at least one of the 2 factors had to be zero itself!

4. Example: Solve. x2+3x-18=0 x2+3x-18=0 Factor the left side
(x+6)(x-3)=0 set each factor =0
x+6=0 OR x-3=0 solve each eqn.
x=-6 OR x=3 check your solutions!

5. Example: Solve. 2t2-17t+45=3t-5
2t2-17t+45=3t-5 Set eqn. =0
2t2-20t+50=0 factor out GCF of 2
2(t2-10t+25)=0 divide by 2
t2-10t+25=0 factor left side
(t-5)2=0 set factors =0
t-5=0 solve for t
+5 +5
t=5 check your solution!

6. Example: Solve. 3x-6=x2-10 3x-6=x2-10 Set = 0
0=x2-3x-4 Factor the right side
0=(x-4)(x+1) Set each factor =0
x-4=0 OR x+1=0 Solve each eqn.
x=4 OR x=-1 Check your solutions!

7. Example: Factor 3x2 −17x+10 1. Factors of (3)(10) that add to −17
2. Factor by grouping
3. Rewrite equation
4. Use reverse distributive
5. Answer
3x2 −17x+10
2. 3x2 −?x −?x+10
3. 3x2 −15x −2x+10
4. 3x(x−5)−2(x−5)
5. (x−5)(3x−2)

8. Example: Factor 3x2 −17x+10 1.Rewrite the equation
2. 3x2 −?x −?x+10 3.
1.Rewrite the equation
2. Factors of (3)(10) that add to −17 (−15 & −2)
3. Place numbers in a box
4. Take our common factors in rows.
5. Take our common factors in columns. x −5
3x2
−15x 3x −2
−2x
+10

9. Finding the Zeros of an Equation
The Zeros of an equation are the x-intercepts !
First, change y to a zero.
Now, solve for x.
The solutions will be the zeros of the equation.

10. Example: Find the Zeros of y=x2-x-6
y=x2-x-6 Change y to 0
0=x2-x-6 Factor the right side
0=(x-3)(x+2) Set factors =0
x-3=0 OR x+2=0 Solve each equation
x=3 OR x=-2 Check your solutions!
If you were to graph the eqn., the graph would cross the x-axis at (-2,0) and (3,0).

11. Assignment
p. 260, odd
35-43 odd,
47-51 odd,
57-69 odd