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polynomials

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polynomials are those which can be of degree 1,2,3 and so on.

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polynomials

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  1. Polynomials and their factors

  2. Polynomials and Polynomial Functions Definitions Term: A number or a product of a number and variables raised to a power. 3 , 5x2 , -2x , 9x2y Coefficient: The numerical factor of each term. Coefficient of x2 in 5x2 is 5. Constant: The term without a variable. 3 , -6 , 5 , 32 Polynomial: A finite sum of terms of the form axn, where a is real number and n is a whole number. -15x3+2x2-5 , 21y6-7y5-2y3+6y

  3. Polynomials and Polynomial Functions Definitions The Degree of a Term with one variable is the exponent on the variable. 5x2 2 , 2x4 4 The Degree of a Term with more than one variable is the sum of the exponents on the variables. -7x2y 3 , 2x4y2 6 The Degree of a Polynomial is the greatest degree of the terms of the polynomial variables. 2x3-3x+7 3 , 2x4y2+5x2y3-6x 6

  4. Polynomials and Polynomial Functions Practice Problems Identify the degrees of each term and the degree of the polynomial: 5x3– 4x2 + 5x4a2b4 + 3a3b5 - 9b4 + 4 3 2 1 6 8 4 0 3 6 4x5y4 + 5x4y6 – 6x3y3 + 2xy 9 10 6 2 10

  5. Polynomials and Polynomial Functions Definitions Monomial: A polynomial with exactly one term. ax2 , rt , 2x4 , -9m , 9x2y Binomial: A polynomial with exactly two terms. x-8 , r-3 , 5x2+2x , -2x + 9x2y Trinomial: A polynomial with exactly three terms. x2 + x -8 , r5+ 3r – 3 , 5x2 + 2x – 7

  6. Polynomials and Polynomial Functions Multiplication Multiplying Monomials by Polynomials Examples: 4x(x2 +4x + 3) = 4x3 + 16x2 + 12x 8x(7x4 + 1) = 56x5 + 8x (-5x3)(3x2– x + 2) = -15x5 + 5x4 – 10x3

  7. Polynomials and Polynomial Functions Practice Problems 1) Evaluate each polynomial function f(-1) where f(x) = 3x2 – 10 . f(-1)= 3(-1)2 – 10 = 3 x 1 – 10 = 3 – 10 = -7 2) Evaluate each polynomial function g(3) where g(x)= 6y2 +11y – 20. g(3) = 6(3)2 + 11(3) – 20 = 6x3x3 +11x3 – 20 = 54 + 33 – 20 = 67

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