MATH 102 Lecture 15: Polynomials

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MATH 102
Ingrid Barbullushi

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Polynomials. Polynomial comes from poly (meaning many) and nomial (in this case meaning term) ... so it says many terms A polynomial can have: constants (like 3, 20, or ) variables (like x and y) exponents (like the 2 in y2), but only 0, 1, 2, 3, ... etc are allowed that can be combined using addition, subtraction, multiplication and division These are polynomials: 3x x 2 6y2 ( 79)x 3xyz + 3xy2z 0.1xz 200y + 0.5 512v5 + 99w5 5 (Yes, 5 is a polynomial, one term is allowed, and it can even be just a constant!) And these are not polynomials 3xy2 is not, because the exponent is 2 (exponents can only be 0,1,2,...) 2(x+2) is not, because dividing by a variable is not allowed 1x is not either x is not, because the exponent is (see fractional exponents) But these are allowed: x2 is allowed, because you can divide by a constant also 3x8 for the same reason 2 is allowed, because it is a constant (= 1.4142...etc) Monomial, Binomial, Trinomial There are special names for polynomials with 1, 2 or 3 terms: monomial, binomial, trinomial Polynomials can have as many terms as needed, but not an infinite number of terms.
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