1. 5.2 Solving Quadratic Equations by Factoring
OBJ: To factor quadratic expressions, solve quadratic equations by factoring, and find zeros of quadratic functions
5.2 Solving Quadratic Equations by Factoring
*To solve a quadratic eqn. by factoring, you must remember
HOW TO FACTOR!
Do Now:
How to Factor handout

2. Zero Product Property
Let A and B be real numbers or algebraic expressions.
If A(B) = 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!

3. Ex 1: 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!

4. Ex 2: 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!

5. Ex 3: 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!

6. 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.
lets try graphing on the calculator:
2nd CALC
option “2:zeros”
left bound? enter
right bound? enter
guess? enter

7. Ex 4: 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).