8-1 Adding and subtracting Polynomials Goals: Add and subtract polynomials. Eligible Content: A1.1.1.5.1

Vocabulary Polynomial – a mathematical expression consisting of a sum of terms. Each term is the product of a constant and one or more variables raised to a positive or zero power. Examples:

vocabulary Standard Form – the terms are in descending order of exponents.

vocabulary Degree – the largest exponent in the polynomial.

vocabulary Constant – degree is zero. Linear – degree is one. Quadratic – degree is two. Cubic – degree is three. Quartic – degree is four.

vocabulary Leading coefficient – the coefficient of the first term when the polynomial is in standard form.

vocabulary Monomial – polynomial with one term. Binomial – polynomial with two terms. Trinomial – polynomial with three terms. Anything bigger – polynomial

Examples Give the degree and classify the polynomial by degree and number of terms. -5 ¼ x -9x+2 x2 – 6 -x3 +2x + 1 3x4 +2x3 – x2 +5x – 8 0, constant, monomial 1, linear, monomial 1, linear, binomial 2, quadratic, binomial 3, cubic, trinomial 4, quartic, polynomial

Addition Add like terms! Put your answer in Standard Form!!

examples

Find (3x2 + 2x – 1) + (–5x2 + 3x + 4). A. –2x2 + 5x + 3 B. 8x2 + 6x – 4 C. 2x2 + 5x + 4 D. –15x2 + 6x – 4

Find (4x3 + 2x2 – x + 2) + (3x2 + 4x – 8). A. 5x2 + 3x – 6 B. 4x3 + 5x2 + 3x – 6 C. 7x3 + 5x2 + 3x – 6 D. 7x3 + 6x2 + 3x – 6

Subtraction Distribute the negative sign! Add like terms and put your answer in Standard Form!!

examples

Find (3x3 + 2x2 – x4) – (x2 + 5x3 – 2x4). A. 2x2 + 7x3 – 3x4 B. x4 – 2x3 + x2 C. x2 + 8x3 – 3x4 D. 3x4 + 2x3 + x2

Find (8y4 + 3y2 – 2) – (6y4 + 5y3 + 9). A. 2y4 – 2y2 – 11 B. 2y4 + 5y3 + 3y2 – 11 C. 2y4 – 5y3 + 3y2 – 11 D. 2y4 – 5y3 + 3y2 + 7

Practice Page 468 #1-18

Homework Pages 468-469 #20 – 42 even