1. Aim: How Do We Solve Quadratic Equations by Factoring
Do Now: Factor: x2+3x-18

2. 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!

3. 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!

4. 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!

5. Solve for x:
3 + x2 – x = 5
x2 – x – 2 = 0
(x – 2)(x + 1) = 0
x = 2, x = –1

6. Solve for x: 2x2 + 4x = 30
2(x2 + 2x – 15) = 0
x2 + 2x – 15 = 0
(x + 5)(x - 3) = 0
x = -5, x = 3

7. Solve x2 – 5x = 0. x(x – 5) = 0 x = 0, x = 5 Solve (x – 5)2 – 100 = 0.
The left side of the equation is the difference of two squares, then factor it into two binomials
[(x – 5) + 10][(x – 5) – 10] = 0
(x +5)(x – 15) = 0
x = -5, x = 15

8. Solve for x: 2x2 – 4x = 12 + x
2x2 – 5x – 12 = 0
(2x + 3)(x – 4) = 0
2x + 3 = 0, x – 4 = 0
x = 4

9. You Try It! Solve the following equations: x2 – 25 = 0 x2 + 7x – 8 = 0
c2 – 8c = 0
5b3 + 34b2 = 7b

10. 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.

11. 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).