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Understanding Adding and Subtracting Polynomials in Algebra

This introduction explores the basics of adding and subtracting polynomials in algebra. Polynomials, composed of terms in the form ax^k, are arranged in standard form with descending degrees. You'll learn how to identify the degree and leading coefficient of polynomials, classify them by the number of terms, and practice writing them in proper form. Through examples, exercises, and attempts, you'll gain a solid understanding of polynomial operations, crucial for advancing in algebra.

reginald-ethelbert
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Understanding Adding and Subtracting Polynomials in Algebra

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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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