Do Now: Journal Explain each of the following rules of exponents: 1.Product of Powers 2.Quotient of Powers 3.Power of Powers 4.Zero Exponent.

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Presentation transcript:

Do Now: Journal Explain each of the following rules of exponents: 1.Product of Powers 2.Quotient of Powers 3.Power of Powers 4.Zero Exponent

January 25, 2013 Adding and Subtracting Polynomials Essential Question: How can I use Polynomials to represent real life situations?

Vocabulary Polynomial – sum of terms in the form of ax k where k is a nonnegtive integer. Example – 2x 3 + 5x 2 -4x + 7 Standard Form – Terms are placed in descending order from largest degree to smallest degree Degree – the degree of each term of a polynomial is the exponent of the variable. Leading Coefficient – When written in its standard form, the coefficient of the first term.

Identify Polynomial Coefficients -4x 2 + x Write the Polynomial in standard form. (Account for each degree) THIS SHOULD BE WRITTEN: X 3 - 4x 2 + 3

POLYNOMIALS MONOMIAL – POLYNOMIAL WITH ONE TERM ( -2X) BINOMIAL – POLYNOMIAL WITH TWO TERMS (3X + 1) TRINOMIAL – POLYNOMIAL WITH THREE TERMS (X 2 + 2X + 6)

Classifying Polynomials by Degree POLYNOMIALDEGREECLASSIFIED BY DEGREE CLASSIFIED BY TERMS 60CONSTANTMONOMIAL 2X1LINEARMONOMIAL 3X + 11LINEARBINOMIAL X 2 + 2X + 52QUADRATICTRIOMIAL 4X 3 + 8X3CUBICBINOMIAL 2X 3 + X 2 – 5x + 13CUBICPOLYNOMIAL

ADDING POLYNOMIALS: LETS REMEMBER LIKE TERMS WE CAN ONLY ADD TERMS WITH LIKE VARIABLES AND LIKE COEFICIENTS

Adding Polynomials Find the sum. Write the answer in standard form. (5x 3 – x + 2 x 2 + 7) + (3x – 4x) + (4x 2 – 8 – x 3 ) Vertical Format: Write each expression in standard form. Align like terms. 5x 3 + 2x 2 – x + 7 3x 2 – 4x + 7 -x 3 + 4x x 3 + 9x 2 – 5x + 6

Subtracting Polynomials Find the difference. (x 2 – 8) – (7x + 4x 2 ) Vertical Format: To subtract, distribute the negative to all terms inside the parenthesis. (X 2 – 8) -(7x + 4x 2 )

Using Polynomials in Real Life You are enlarging a 5 inch by 7 inch photo by a scale factor of x and mounting it on a mat. You want the mat to be twice as wide as the enlarged photo and 2 inches less than twice as high as the enlarged photo. a.Draw a digram to represent the described situation. b.Write a model for the area of the mat around the photograph as a function of the scale factor.

Using Polynomials in Real Life The dimensions of the photo are enlarged by a scale factor of x 5x 7x 10x 14x -2