1. 5.2: Solving Quadratic Equations by Factoring (p. 256)

2. 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. x 2 +3x-18=0 x 2 +3x-18=0Factor the left side (x+6)(x-3)=0set each factor =0 x+6=0 OR x-3=0solve each eqn. -6 -6 +3 +3 x=-6 OR x=3check your solutions!

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

6. Example: Solve. 3x-6=x 2 -10 3x-6=x 2 -10Set = 0 0=x 2 -3x-4Factor the right side 0=(x-4)(x+1)Set each factor =0 x-4=0 OR x+1=0 Solve each eqn. +4 +4 -1 -1 x=4 OR x=-1 Check your solutions!

7. 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.

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

9. Assignment