A right triangle is shown below. The Pythagorean Theorem says that the length of

Question

A right triangle is shown below. The Pythagorean Theorem says that the length of the longest side of the triangle, side c, is related to the lengths of the sides of the other two sides, sides a and b as follows: a2+b2=c2 If side a =1 and side b = 2 then c2=12+22 c2=1+4 c2=5 c=V3 1.) Listed below is the length of side c of a right triangle. Find the possible lengths of sides a and b of the triangle. Your answers should be whole numbers. sqrt{}40 2.) Multiple/simplify as needed. Assume all exponents are positive integers and none of the bases equal zero. Explain the steps. (an+bn)(an-bn) 3.) How would you factor 6x^2 - x - 15?

**Please solve step 3

Explanation / Answer

1). There is no image and no listing of the length of side c of a right triangle. However, if c = 40, then c2 = 40 so that a2+b2 =40. If a and b are whole numbers, then the only possible solutions are as under:

A. a = 4, b = 6

B. a = 6, b =4.

No other solution will give whole numbers for a and b.

2) let an = x and bn = y. Then, (an+bn)(an-bn) = (x+y)(x-y) = x2-y2 = a2n –b2n.

3) We have 6x2-x-15 = 6x2-10x+9x -15 = 2x(3x-5) +3( 3x-5) = (3x-5)(2x+3).

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