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Exponents

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Ex. (-2a 2 b 3 )(-4ab 2 ) Ex. (3ab 2 ) 4 Ex. (-2a 2 b) 3 (-3ab 2 ) 2

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Ex. x 2n x 2n Ex.

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Ex. (2x -3 y 3 ) 2 Ex.

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A monomial is a number, variable, or a product of these x 3x23x2 4x2y4x2y The degree of a monomial is the sum of the powers of the variables Polynomials

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5x35x3 5 is the coefficient x is the base 3 is the exponent or power

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A polynomial is an expression made up of the sum of monomials, called terms 3x 2 monomial 4x 2 y binomial x 4 – 5x + 6 trinomial The degree of a polynomial is the greatest of the degrees of the terms

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P(x) = 7x 4 – 3x 2 + 2x – 4 This is a polynomial function 7, -3, 2, and -4 are called coefficients Note that the terms are in descending order with respect to powers 7 is called the lead coefficient because it is the coefficient for the largest power of x -4 is called the constant term because it is not multiplied by the variable

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Coefficients can be any real number, but powers of a polynomial must be whole numbers (no negatives or fractions)

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Ex. If P(x) = -5x 3 + x 2 + 3x – 2, find: a) P(-1) b) P(2) c) The degree of P(x) d) The lead coefficient of P(x)

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When adding and subtracting polynomials, combine like terms (same variables to the same powers) Ex. (4x 2 + 3x – 5) + (x 2 – 7x + 10) Ex. (5x 2 – x + 6) – (-2x 2 + 3x – 11)

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Ex. (3a 3 – b + 2a – 5) + (a + b + 5) Ex. (12z 5 – 12 z 3 + z) – (-3z 4 + z z)

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Multiplying Polynomials Ex. -5y 2 (3y – 4y 2 ) Ex. 3a + 2a(3 – a) Ex. 2a 2 b(4a 2 – 3ab + 2b 2 )

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When multiplying bigger polynomials, be sure each term is paired up Ex. (x + 2)(x 2 – 3x – 6)

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Multiplying a binomial by a binomial can be organized by remembering FOIL (3x – 2)(2x + 5) First Outer Inner Last 6x26x2 15x -4x -10 6x x – 10

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Ex. (6x – 5)(3x – 4) Ex. (2x 2 – 3)(x 2 – 2) Ex. (3x – 2y)(2x + y)

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Sum and Difference of Two Terms: (a + b)(a – b) = Ex. (2x – 1)(2x + 1)

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Square of a Binomial: (a + b) 2 = Ex. (5x – 3y) 2

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