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Section 6.6: Solving Equations by Factoring Worksheet 6.6

The Zero Factor Property: If $ab=0$, then either $a=0$ or $b=0$.

Example: Solve the equation $(2x-3)(x+5)=0$

Example: Solve the equation $x^2-3x+2=0$











Examples

$56r^2-82r+30=0$

$12u^2=32u+35$













Using Graphs to Solve Quadratic Equations

Example: Use the graph of $y=−x^2+3x+4$ below to solve the equation $−x^2+3x+4=0.$














Constructing Equations with Given Roots

Example: Construct a quadratic equation having roots $x=-2$ and $x=3$

Example: Construct a quadratic equation with the following solutions: $\gamma=-\frac{17}{2}$ or $\gamma=-\frac{11}{7}$.













Application Involving Area

Example: The base of the triangle shown in the figure is 10 cm longer than the height. Determine the height of the triangle if its area is 48 cm2.