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Introduction to Adding and Subtracting Polynomials: Standard Form and Classification

This lesson provides an introduction to adding and subtracting polynomials, covering essential concepts such as polynomial definitions, standard form, degree classification, and leading coefficients. Students will learn to recognize and classify polynomials by their degree and number of terms, including classifications such as monomials, binomials, and trinomials. The lesson features examples of adding and subtracting polynomials, along with practice problems to reinforce these skills. Perfect for students looking to deepen their understanding of polynomial operations.

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Introduction to Adding and Subtracting Polynomials: Standard Form and Classification

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  1. Algebra 10.1 Adding and Subtracting Polynomials

  2. Intro • Polynomial-the sum of terms in the form axk where k is a nonnegative integer. • A polynomial is usually written in standard form meaning the terms are placed in descending order by degree(exponent). -4x3 + 5x2 – 4x + 9 12x – 8x2 + 6 The degree of a polynomial is the largest exponent. Leading coefficient This is a polynomial of degree 3.

  3. TermsName 1 2 3 >3 Binomial Monomial DegreeName 0 1 2 3 Classifying Polynomials Constant Linear Trinomial Polynomial Quadratic Cubic Name by Number of terms Degree # Degree Name Polynomial 0 constant monomial 6 1 linear monomial -2x 1 linear 3x + 1 binomial quadratic trinomial -x2 + 2x – 5 2 3 cubic 4x3 – 8x binomial quartic polynomial 2x4 – 3x2 + 4x – 7 4

  4. Writing a Polynomial in Standard Form • Let’s try: 4x – 3x3 + 2x2 – 9 Standard form: -3x3 + 2x2 + 4x – 9 • You try: -9x + 3 + 4x2 – 10x4 Standard form: -10x4 + 4x2 – 9x + 3 Classify this polynomial by degree. Cubic -10 What is the leading coefficient?

  5. Adding Polynomials Let’s try: (6x2 – x + 3) + (-2x + x2 – 7) + (4x + 2) Answer: 7x2 + x - 2 Trinomial Classify this polynomial by the number of terms. You try: (-8x3 + x – 9x2 + 2) + (8x2 – 2x + 4) + (4x2 – 1 – 3x3) -11 What is the leading coefficient? Answer: -11x3 + 3x2 - x + 5

  6. Subtracting Polynomials Let’s try: (-6x3 + 5x – 3) – (2x3 + 4x2 – 3x + 1) (-6x3 + 5x – 3) + (-2x3– 4x2+ 3x – 1) Answer: -8x3 - 4x2 + 8x - 4 You try: (12x – 8x2 + 6) – (-8x2 – 3x + 4) (12x – 8x2 + 6) + (8x2+ 3x – 4) Answer: 15x + 2 Classify this polynomial by degree. Classify this polynomial by the # of terms. Linear Binomial

  7. HW • P. 579 – 580 (13-29 odd, 53-60, 73-78)

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