1. 4.4: Factoring (Quadratic Equations) Algebra II

2. Ex. 1 15x² - 2x - 8

3. Ex. 2 Check for GCF 18z²+36z+16

4. 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.” FACTORING WHEN THE LEADING COEFFICIENT IS NOT 1 AND A FACTORING PATTERN IS NOT EVIDENT Ex. 3

5. Steps for Solving Quadratic Equations 1.) Set Quadratic equation equal to zero. 2.) Factor out GCF if one exists. 3.) Factor completely. 4.) Set each monomial & binomial equal to zero. 5.) Solve for variable.

6. Example 1): 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!

7. Example 2): 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!

8. Example 3

9. Assignment

10. 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!

11. 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.

12. Example 4): 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).

13. Example 1): 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!

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

15. 4.4B: Solving (Quadratic Equations) by Factoring Algebra II