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Explaining Rules of Exponents and Adding/Subtracting Polynomials

Learn the rules of exponents and how to add/subtract polynomials. Understand terms, coefficients, degrees, and standard form. Solve real-life polynomial problems.

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Explaining Rules of Exponents and Adding/Subtracting Polynomials

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  1. Do Now:Journal Explaineach of the followingrules of exponents: Product of Powers Quotient of Powers Power of Powers ZeroExponent

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

  3. Vocabulary Polynomial – sum of terms in the form of axk where k is a nonnegtive integer. Example – 2x3 + 5x2 -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.

  4. Identify Polynomial Coefficients -4x2 + x3 + 3 Write the Polynomial in standard form. (Account for eachdegree) THIS SHOULD BE WRITTEN: X3 - 4x2 + 3

  5. POLYNOMIALS MONOMIAL – POLYNOMIAL WITH ONE TERM ( -2X) BINOMIAL – POLYNOMIAL WITH TWO TERMS (3X + 1) TRINOMIAL – POLYNOMIAL WITH THREE TERMS (X2 + 2X + 6)

  6. Classifying Polynomials by Degree

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

  8. Adding Polynomials Find the sum. Write the answer in standard form. (5x3– x + 2 x2 + 7) + (3x2 + 7 – 4x) + (4x2 – 8 – x3) Vertical Format: Write each expression in standard form. Align like terms. 5x3 + 2x2 – x + 7 3x2 – 4x + 7 -x3 + 4x2 - 8 4x3 + 9x2 – 5x + 6

  9. Subtracting Polynomials Find the difference. (x2 – 8) – (7x + 4x2) Vertical Format: To subtract, you add the opposite. You can multiply each term in the subtracted polynomial by -1 and add. (X2 – 8) x2 -8 -(7x + 4x2) + -4x2 -7x_____ - 3x2 - 7x - 8

  10. Using Polynomials in Real Life You are enlarging a 5 inch by 7 inch photo by a scale facto of x and mountingit on a mat. You want the mat to betwice as wide as the enlarged photo and 2 incheslessthantwice as high as the enlarged photo. • Draw a digram to represent the described situation. • Write a model for the area of the mat around the photograph as a function of the scale factor.

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

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