## Inequalities Signs

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You know you flip the inequality sign when you divide or multiply be a negative.
3(x-1)<12 when you solve you get x<5 but if you changed the 3 to a -3 the solution would become x>-5 where you would flip the sign from < to >

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Factoring Polynomials of Degree 3 Factoring a 3 - b 3 An expression of the form a 3 - b 3 is called a difference of cubes. The factored form of a 3 - b 3 is (a - b)(a 2 + ab + b 2) : (a - b)(a 2 + ab + b 2) = a 3 - a 2 b + a 2 b - ab 2 + ab 2 - b 3 = a 3 - b 3 For example, the factored form of 27x 3 - 8 ( a = 3x, b = 2 ) is (3x - 2)(9x 2 + 6x + 4) . Similarly, the factored form of 125x 3 -27y 3 ( a = 5x, b = 3y ) is (5x - 3y)(25x 2 +15xy + 9y 2) . To factor a difference of cubes, find a and b and plug them into (a - b)(a 2 + ab + b 2) . Factoring a 3 + b 3 An expression of the form a 3 + b 3 is called a sum of cubes. The factored form of a 3 + b 3 is (a + b)(a 2 - ab + b 2) : (a + b)(a 2 - ab + b 2) = a 3 + a 2 b - a 2 b - ab 2 + ab 2 + b 3 = a 3 - b 3 .

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Applying the Fundamental Concepts of Algebra An understanding of the fundamental concepts of algebra and of how those fundamental concepts may be applied is necessary in many professional and most technical careers. For engineers and scientists it is an essential requirement. The fundamental concepts of algebra are described in the preceding section of this article. How these concepts may be applied to aid in the solution of various types of mathematical problems is explained here. USING REAL NUMBERS

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