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

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!

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

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

Example: Solve.
3x-6=x 2 -10
3x-6=x 2 -10
0=x 2 -3x-4
Set = 0
Factor 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!

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

Example: Find the Zeros of y=x 2 -x-6 y=x 2 -x-6
0=x 2 -x-6
Change y to 0
Factor the right side
0=(x-3)(x+2) Set factors =0 x-3=0 OR x+2=0 Solve each equation
+3 +3 -2 -2 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).