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Polynomials

# Polynomials - POLYNOMIALS Denition 1 A real polynomial is...

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POLYNOMIALS Definition 1: A real polynomial is an expression of the form P ( x ) = a n x n + a n - 1 x n - 1 + · · · + a 1 x + a 0 where n is a nonnegative integer and a 0 , a 1 , . . ., a n - 1 , a n are real numbers with a n = 0. The nonnegative integer n is called the degree of P . The numbers a 0 , a 1 , . . ., a n - 1 , a n are called the coefficients of P ; a n is called the leading coefficient . Examples: Polynomials of degree 0: The non-zero constants P ( x ) a . Note: P ( x ) 0 (the zero polynomial) is a polynomial but no degree is assigned to it. Polynomials of degree 1: Linear polynomials P ( x ) = ax + b . The graph of a linear polynomial is a straight line. Polynomials of degree 2: Quadratic polynomials P ( x ) = ax 2 + bx + c . The graph of a quadratic polynomial is a parabola which opens up if a > 0, down if a < 0. Polynomials of degree 3: Cubic polynomials P ( x ) = ax 3 + bx 2 + cx + d . Polynomials of degree 4: Quartic polynomials P ( x ) = a 4 x 4 + a 3 x 3 + a 2 x 2 + a 1 x + a 0 .

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Polynomials - POLYNOMIALS Denition 1 A real polynomial is...

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