Factoring Polynomials

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The Pythagorean Theorem

Example

Continued

1.) Understand

Read and reread the problem. If we let

x = the length of the shorter leg, then

x + 10 = the length of the longer leg and

2x – 10 = the length of the hypotenuse.

Slide 66

The Pythagorean Theorem

Example continued

2.) Translate

Continued

By the Pythagorean Theorem,

(leg a)2 + (leg b)2 = (hypotenuse)2

x2 + (x + 10)2 = (2x – 10)2

3.) Solve

x2 + (x + 10)2 = (2x – 10)2

Slide 67

The Pythagorean Theorem

Example continued

4.) Interpret

Check: Remember that x is suppose to represent the length of the shorter side. So, although x = 0 satisfies our equation, it cannot be a solution for the problem we were presented.

If we let x = 30, then x + 10 = 40 and 2x – 10 = 50. Since 302 + 402 = 900 + 1600 = 2500 = 502, the Pythagorean Theorem checks out.

State: The length of the shorter leg is 30 miles. (Remember that is all we were asked for in this problem.)