Introduction to Polynomials

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7.1 An Introduction to Polynomials

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Presentation transcript:

Introduction to Polynomials CCM2 11-1

Monomials and degree Monomials (or terms) are the product of real numbers and variables. Each variable has an exponent called a power. The number at the front of the variables is called the coefficient. When no coefficient is shown it is “1.” The degree of a monomial is the sum of the exponents of the variables. Remember when no exponent is shown, it is “1.” Examples: x2 6xy 2x3y 4 Example: x2 6xy 2x3y 4 Coefficient: 1 6 2 n/a Degree: 2 2 4 0

Monomial and Term Names Monomials are named by their degree Degree Name Example Constant 5 1 Linear Term 3x 2 Quadratic Term 4x2 3 Cubic Term 2x3 4 Quartic Term 6x4 5th-Degree Term 3x5

polynomials and degree Polynomials are the sum or difference of monomials. The degree of a polynomial is the same as its highest degree term. This term determines the polynomials overall shape. Examples: x2 - 6x + 8 or 2x3y - 4 Example: x2 + 6x + 8 2x3y + 4 Degree: 2 4

Classifying Polynomial Classify Polynomials by degree and number of terms. The degree name is that of its highest degree term. The number of terms are described as follows Number of Terms Name Example 1 Monomial 5x 2 Binomial 3x2 + 7 3 Trinomial 4x2 + 2x + 1

You Try Classify the following Polynomials Example Name 5x Linear Monomial 3x2 -2x + 7 Quadratic Trinomial 2x + 1 Linear Binomial 5x4 - 2 Quartic Binomial 3x3 -5x + 7 Cubic Trinomial

Standard Form Arrange the terms starting with the highest degree term and ending with the lowest degree term. For example: x2 + 7 – 4x becomes x2 – 4x +7 The coefficient of the highest degree term is called the “Leading Coefficient” because it is the first coefficient of the polynomial in standard form. It determines how wide or narrow the polynomial is, with numbers closer to 0 being wider.

ADDING or subtracting Polynomials (Horizontal Method) If subtracting, distribute the negative first Combine like terms (like terms have the same variables and powers.) Example: (x2 + 6x + 8) - (3x - 2) x2 + 6x + 8 - 3x + 2 x2 + 3x + 10

ADDING or subtracting Polynomials (Vertical Method) Write one polynomial over the other like you would for numbers. Make sure to align like terms in the same columns Add or subtract each column as indicated x2 + 6x + 8 + 3x - 2 x2 + 9x + 6 x2 + 6x + 8 - 3x - 2 x2 + 3x +10

Summary Identified the key parts of a polynomial Classified polynomials Add and subtract polynomials Horizontal Method Vertical Method Thank You