mac1140_lecture2_1

mac1140_lecture2_1 - L2 1.3 Polynomials; Binomial Theorem...

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11 L2 §1.3 Polynomials; Binomial Theorem Rules for Exponents Product Rule : For all positive integers , mn and every real number a : m n aa a + = Example . Find the following products: 63 zz ⋅= 21 2 23 (2 ) (2 ) xx π ++ = 37 4 (7 )(2 ) x y x y = Definition : For any nonzero real number a , 0 1 a = Note : expression 0 0 is undefined. Example . Evaluate each power: 0 ) −= vs. 0 7 = 0 22 ( 3 ) −− + − =
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12 Power Rules : For all positive integers m and n and all real a and b , () mn m n aa = mm m ab a b = 0 m m m b bb ⎛⎞ =≠ ⎜⎟ ⎝⎠ Example . Simplify: 722 bc −= 32 3 2 2( ) xz xz 5 2 40 3 xy zw = Caution! 3 ab vs. 3 ab 2 ab + vs. 22 +
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13 Polynomials Definition: A polynomial is a term or a finite sum of terms, with only nonnegative integer exponents permitted on the variables. The d egree of a polynomial in one variable is the greatest exponent in the polynomial. A polynomial containing exactly 1 term – a monomial 2 te rm s a b inom ia l 3 s a t r l Adding and Subtracting Polynomials: To add/subtract polynomials, add/subtract coefficients of like terms.
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mac1140_lecture2_1 - L2 1.3 Polynomials; Binomial Theorem...

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