Do Now Journal Explain each of the following

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 axk where k is a nonnegtive integer. Example – 2 x 3 + 5 x 2 -4 x + 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 -4 x 2 + x 3 + 3 Write the Polynomial in standard form. (Account for each degree) THIS SHOULD BE WRITTEN: X 3 - 4 x 2 + 3

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

Classifying Polynomials by Degree POLYNOMIAL DEGREE CLASSIFIED BY TERMS 6 0 CONSTANT MONOMIAL 2 X 1 LINEAR MONOMIAL 3 X + 1 1 LINEAR BINOMIAL X 2 + 2 X + 5 2 QUADRATIC TRIOMIAL 4 X 3 + 8 X 3 CUBIC BINOMIAL 2 X 3 + X 2 – 5 x + 1 3 CUBIC POLYNOMIAL

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

Subtracting Polynomials Find the difference. (x 2 – 8) – (7 x + 4 x 2) Vertical Format: To subtract, you add the opposite. You can multiply each term in the subtracted polynomial by -1 and add. (X 2 – 8) -(7 x + 4 x 2) x 2 -8 + -4 x 2 -7 x_____ - 3 x 2 - 7 x - 8

Using Polynomials in Real Life You are enlarging a 5 inch by 7 inch photo by a scale facto 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 7 x 5 x 10 x 14 x -2