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Friday 23rd of June
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 Depdendent Variable

 Number of equations to solve: 23456789
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 Dependent Variable

 Number of inequalities to solve: 23456789
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## Factoring

Some Common Factoring Patterns

x 2 - a 2 = (x - a) Â· (x + a) â€œDifference of two squaresâ€

x 2 + 2 Â· a Â·  x + a 2 = (x + a) 2 â€œPerfect square Iâ€

x 2 - 2 Â· a Â· x + a 2 = (x - a) 2 â€œPerfect square IIâ€

The objective of solving a quadratic equation:

a Â· x 2 + b Â· x + c = 0,

is to find the values of x that make the quadratic formula equal to zero. Graphically, these x-values are the x-coordinates of the points where the graph of

y = a Â· x 2 + b Â· x + c

crosses the x-axis (see Figure 2).

When you are trying to solve the quadratic equation a Â· x 2 + b Â· x + c = 0, then what you are trying to do is to find the x-coordinates of any points where the graph of  y = a Â· x 2 + b Â· x + c crosses the x-axis.

Figure 2: The solutions of a quadratic equation are the x-coordinates

of the points where the graph of the quadratic cuts through the x-axis.