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Algebra

Algebra. 10.1 Adding and Subtracting Polynomials. Intro. Polynomial- the sum of terms in the form ax k 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). -4x 3 + 5x 2 – 4x + 9.

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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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