1. 4.3: Solving (Quadratic Equations) by Factoring
Algebra II

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

3. Ex. 1 Factor the expression
1b.)

4. Special Factoring Patterns
Difference of Two Squares
Perfect Square Trinomial

5. Ex. 2
2a.)
2b.)
2c.)

6. 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!

7. Ex. 3): 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!

8. 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.

9. Example 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).

10. Assignment

11. Example 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!

12. Example 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!

13. Multiply leading coefficient and constant.
FACTORING WHEN THE LEADING COEFFICIENT IS NOT 1 AND A FACTORING PATTERN IS NOT EVIDENT
Multiply leading coefficient and constant.
Now find factors of -80 that yield a sum of -11.
Divide the constants by the leading coefficient from above.
Clean it up. (Reduce what you can.)
Move any remaining denominators to the front of the variable.
Check by “foiling.”