4.3: Solving (Quadratic Equations) by Factoring Algebra II

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

Ex. 1 Factor the expression 1b.)

Special Factoring Patterns Difference of Two Squares Perfect Square Trinomial

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

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!

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. -6 -6 +3 +3 x=-6 OR x=3 check your solutions!

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.

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 +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).

Assignment

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!

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. +4 +4 -1 -1 x=4 OR x=-1 Check your solutions!

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.”