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5 .3 – Polynomials and Polynomial Functions

5 .3 – Polynomials and Polynomial Functions. Definitions. Term : a number or a product of a number and variables raised to a power. Coefficient : the numerical factor of each term. Constant : the term without a variable. Polynomial : a finite sum of terms of the form a x n , where a is a

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5 .3 – Polynomials and Polynomial Functions

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  1. 5.3 – Polynomials and Polynomial Functions Definitions Term: a number or a product of a number and variables raised to a power. Coefficient: the numerical factor of each term. Constant: the term without a variable. Polynomial: a finite sum of terms of the form axn, where a is a real number and n is a whole number.

  2. 5.3 – Polynomials and Polynomial Functions Definitions Monomial: a polynomial with exactly one term. Binomial: a polynomial with exactly two terms. Trinomial: a polynomial with exactly three terms.

  3. 5.3 – Polynomials and Polynomial Functions Definitions The Degree of a Term with one variable is the exponent on the variable. The Degree of a Term with more than one variable is the sum of the exponents on the variables. The Degree of a Polynomial is the greatest degree of the terms of the polynomial variables.

  4. 5.3 – Polynomials and Polynomial Functions Practice Problems Identify the degrees of each term and the degree of the polynomial. 8 8 10 10

  5. 5.3 – Polynomials and Polynomial Functions Practice Problems Evaluate each polynomial function

  6. 5.4 – Polynomials and Polynomial Functions Multiplication Multiplying Monomials by Monomials Examples:

  7. 5.4 – Polynomials and Polynomial Functions Multiplication Multiplying Monomials by Polynomials Examples:

  8. 5.4 – Polynomials and Polynomial Functions Multiplication Multiplying Two Polynomials Examples:

  9. 5.4 – Multiplying Polynomials Special Products Multiplying Two Binomials using FOIL First terms Outer terms Inner terms Last terms

  10. 5.4 – Multiplying Polynomials Special Products Multiplying Two Binomials using FOIL First terms Outer terms Inner terms Last terms

  11. 5.4 – Multiplying Polynomials Special Products Squaring Binomials

  12. 5.4 – Multiplying Polynomials Special Products Multiplying the Sum and Difference of Two Binomials

  13. 5.4 – Multiplying Polynomials Special Products Dividing by a Monomial

  14. Extra Problems

  15. 5.4 – Polynomials and Polynomial Functions Multiplication Multiplying Two Polynomials Examples:

  16. 5.4 – Polynomials and Polynomial Functions Multiplication Multiplying Two Polynomials Examples:

  17. 5.4 – Polynomials and Polynomial Functions Multiplication Multiplying Two Polynomials Examples:

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