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Adding and Subtracting Polynomials: Easy Methods for Effective Results

Learn to add and subtract polynomials effortlessly with clear explanations and examples. Identify terms, degrees, and coefficients with confidence. Master the vertical format for clear computations.

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Adding and Subtracting Polynomials: Easy Methods for Effective Results

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  1. Homework for 9-1 p.557 2, 5, 8, 19, 22, 25, 26, 28, 30, 34, 38, 40, 48, 54

  2. 9-1 Add & Subtract Polynomials Objective: add and subtract polynomials

  3. Vocabulary • Monomial • A number, variable, or the product of a number and one or more variables with whole number exponents. • Its degree is the sum of the exponents of the variables.

  4. Vocabulary • Monomial: What is NOT one

  5. Vocabulary • Polynomial: a monomial or a sum of monomials, each called a term • Degree of a Polynomial: the greatest degree of its terms • Leading Coefficient: the coefficient of the first term when the terms are written so the exponents decrease from left to right. • Binomial: Polynomial with two terms • Trinomial: Polynomial with three terms

  6. Polynomials • -2b4 + 3b3 + b2 • Degree = 4 • Lead Coeff. = -2 • 3b3-2b4 + b2 • Write so that the exponents decrease from left to right. • Identify the degree. • Identify the leading coefficient.

  7. Identify & ClassifyPolynomial? Degree? Classify… • 5xy2 • 3a-5 • X4 + 3x3 – x • 9/m • 6a2c + 5ac5 • Yes, 3, monomial • Yes, 1, binomial • Yes, 4, polynomial • No • Yes, 6, binomial

  8. Add Polynomials • Just combine like terms! • (-2x2 + 3x – x3) + (3x2 + x3 – 12) • X2 + 3x -12 • (4x3 + 2x2 -4) + (x3 -3x2 + x) • 5x3 – x2 + x - 4 • Vertical Format • 4x3 + 2x2 -4 • x3 -3x2 + x • 5x3 – x2 + x - 4

  9. Subtract Polynomials • (2c2 – 8) – (3c2 – 4c +1) • 2c2 – 8 – 3c2 + 4c – 1 • -c2 + 4c – 9 • (5y2 + 2y – 4) – (-y2 +4y – 3) • 5y2 + 2y – 4 + y2 - 4y + 3 • 6y2 – 2y - 1 • Vertical Format • (5y2 + 2y – 4) 5y2 + 2y – 4 • (-y2 +4y – 3) y2 - 4y +3 • 6y2 – 2y - 1

  10. TV • Between 1999 and 2005, the number of hours an individual person watched broadcast television B and cable and satellite television C can be modeled by: B = 2.8t2 – 35t + 879 and C = -5t2 + 80t +712 where t is the number of years since 1999. About how many hours did people watch television is 2002? • About 1706 hours

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