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 Leading coefficient The degree of a polynomial is the largest exponent. This is a polynomial of degree 3. 12x – 8x 2 + 6

Classifying Polynomials Polynomial Degree #Degree Name Name by Number of terms 6 0constantmonomial -2x 1linearmonomial 3x + 1 1linear binomial -x 2 + 2x – 52 quadratictrinomial 4x 3 – 8x 3cubic binomial 2x 4 – 3x 2 + 4x – 74 quarticpolynomial Terms Name >3 Degree Name Monomial Constant Binomial Trinomial Polynomial Linear Quadratic Cubic

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

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

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

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