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8.1: Adding & Subtracting Polynomials

Learn about polynomials, terms, degrees, and standard forms. Practice adding, subtracting, and solving word problems. Get ready for homework with examples and exercises.

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8.1: Adding & Subtracting Polynomials

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  1. 8.1: Adding & Subtracting Polynomials Algebra 1

  2. Vocabulary Polynomial: a monomial or the sum of monomials, each called a term of the polynomial.

  3. Vocabulary Classifying a Polynomial by the Number of Terms Monomial: one term Ex: Binomial: two terms Ex: Trinomial: three terms Ex:

  4. Finding the Degree of a Monomial and Polynomial Monomial: Single variable: Exponent is the degree Ex: , Degree is 3 Multi variable: the sum of the exponentsof all its variables. Ex: , Degree is 3 (A nonzero constant term has a degree of 0.) Polynomial: Single variable: Highest exponent is the degree Ex: , Degree is 2 Multi variable: the sum of the exponents in each term. Ex: , Degree is 15

  5. Standard Form and Leading Coefficient Standard form of a polynomial: the terms are written in order from greatest to leastdegree. Leading coefficient: when written in standard form, the coefficient of the first term.

  6. Example 1: Write answer in standard form. Add the polynomials. Then find the degree of polynomial. *Add the coefficients, leave exponents the same. a) (7y2 + 2y – 3) + (2 – 4y + 5y2)

  7. Example 1: Write answer in standard form. Add the polynomials. Then find the degree of polynomial. *Add the coefficients, leave exponents the same. b) (4x2 – 2x + 7) + (3x – 7x2– 9)

  8. Example 2: Subtract the polynomials.Then find the degree of polynomial. a) (6y2 + 8y4 – 5y) – (9y4 – 7y + 2y2)

  9. Example 2: Subtract the polynomials. Then find the degree of polynomial. b) (6n2 + 11n3 + 2n) – (4n – 3 + 5n2)

  10. Example 3: Word Problem The profit a business makes is found by subtracting the cost to produce an item C from the amount earned in sales S. The cost to produce and the sales amount could be modeled by the following equations, where x is the number of items produced. C = 100x2 + 500x – 300S = 150x2 + 450x + 200 a) Find an equation that models the profit. b) Use the above equation to predict the profit if 30 items are produced and sold.

  11. Exit Slip Find

  12. Homework • Page 468: 1-9 odd, 15-19, 55-57

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