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Transcript
Warm Up Please complete at the top of your notes. Be sure to include the question itself. Use the polynomial 6x2 – 4x + 8 to identify the following: Coefficient(s):__________ Constant(s):__________ Base(s):__________ Operator(s):__________ Degree of the polynomial:__________ Categorize the polynomial by the number of terms:__________ Categorize the polynomial by the degree:__________ Lead coefficient:__________ Polynomials Reintroducing parts of polynomials and Operating with polynomials Polynomials can be defined as the sum or difference of terms or expressions. Each term can be either a constant or variable, have one or more terms, and be composed of like terms or different terms. The expressions that can exist in a polynomial are defined as: Integer- a negative or positive whole number including zero. Constants – A single number in the equation that does not contain any variable. Example: 4, 6, -20 Coefficient – The numerical part of a monomial. Example: -5, -4, … -1, 0, 1, … 5, 6, 7 …etc… Example: 7 is the coefficient of 7x3y Degree – The highest power to which a variable is raised. Examples: Identify each term in the following polynomial: 2x3 - 4 *copy ALL of this slide → the single number in the equation Constant: 4 Coefficient: 2 →the number in front of the variable x Degree: 3 →the highest power of the variable Give the degree of the following polynomial: 5x6 – 3x4 – 11x2 + 8 *copy ALL of this slide Degree: 6 It is a sixth degree polynomial because the highest exponent of x is 6. → There are also different types of polynomials: Monomial – A constant, or the product of a constant, and one or more variables raised to an integer. Example: Polynomial – Any finite sum (or difference) of terms. Example: 4x2 – 66x + 3y – 22z Binomial – A polynomial consisting of exactly two terms. -3x2y3z Example: 27x− 3x3 Trinomial – A polynomial consisting of exactly three terms. Example: 3x4 + 2x2 - 20 Break - Quadratics The is standard form of a quadratic equation ax2 + bx + c = 0 Can *copy ALL of this slide you identify a, b, and c? 2 1)2x + 4 – 12x = 0 2)x2 = -2x + 3 3)4x2 – 2x = 0 2 4)3x – 2 = -3x There are special binomial rules that can be followed that can make them easier to solve. *copy ALL of this slide Combining like Terms Polynomials can be short expression or really long ones. Probably the most common thing you will be doing with polynomials is combining like terms in order to simplify long polynomial expressions. Combining “like terms” is the process by which we combine exact same terms containing the same variable with the same exponent together to shorten the expression. Examples *copy ALL of this slide Evaluating Polynomials *copy ALL of this slide To evaluate polynomials substitute the given value and solve the equation. Example: Break: factor puzzle Addition and Subtraction of Polynomials The addition and subtraction of polynomials consist of combining like terms by grouping together the same variable terms with the same degrees. In the case of subtraction, if the subtraction sign (or negative sign) is outside parentheses, the first thing to do is to distribute the negative sign to each of the terms inside the parentheses. Examples: *copy ALL of this slide Examples: *copy ALL of this slide Multiplication of Polynomials To multiply polynomials the same rules apply as with exponents since we are dealing with variables with different exponents. Remember that when multiplying, the exponents add together. Examples: *copy ALL of this slide Examples: *copy ALL of this slide Division of Polynomials When dealing with polynomials divided by a single term the division can be treated as a simplification problem and the action is just to reduce its terms to the lowest possible. Examples: 10 in Ten You will solve 10 problems in ten minutes Your score will be the number correct Through the course of the quarter. We will have approximately 15 of these. Your grade will be the combined points out of 100. This means there are about 150 points possible… If you are absent, you do not get to take the 10 in Ten 10 in Ten - I