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Factoring Polynomials of Degree 3

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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 .

Words for Operations

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Handout Module 2 Review ? Words for Operations Subtraction Minus Difference between From Less Less than Fewer than Decreased by Take away ?a number minus 2? ?the difference between a number? ?2 from a number? ?a number less 3? ?2 less than a number? ?2 fewer than a number? ?a number decreased by 2? ?a number take away 2? x ? 2 x ? 8 n ? 2 n ? 3 y ? 3 y ? 2 x ? 2 x ? 2 Addition Plus And Added to Greater than More than Increased by Total Sum of ?a number plus 2? ?3 and a number? ?8 added to a number? ?3 greater than a number? ?3 more than a number? ?a number increased by 2? ?the total length? ?the sum of the length and width? x + 2 3 + n x + 8 n + 3 y + 3 y + 2 l1 + 12 + ? l + w Multiplication Times Product At double, triple, etc. Twice Of (fractions of)

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