Polynomial definitions Al gebraic expression -numbers and/or variables with operations 2a + 4 3r6y  7 term: numbers or variables separated by a + sign in an algebraic expression

polynomial- an expression with more than two terms Polynomial A. Classified by Number of Terms 1.) monomial: an expression that is a constant, a variable or the product of both with variables having whole number exponents (an expression with one term) 4x2-7ab-82x3y 2.) binomial - an expression with two terms 5y + 33b2 - 9a 3.) trinomial - a polynomial with three terms 3x4 + 2x +12w3 + 6w - 9 *greater than three terms does not have a special name 3x4 + 2x + 1 4x4 + 2x3 + 2x + 1

Monomial binomial trinomial Place the polynomials in the correct box 2x 3y2 9 3w y + 1 y3 + 6 y2 + y - 7 x3 - x2 - x

Degree of each term - the exponent of the variable Degree of the polynomial - the largest degree of its terms Degree B. Classified by degree 1.)constant - a monomial that is a numeral; an expression that does not have a variable ) Linear- a term or polynomial with the variable raised to the first power 4x6y34tw ) Quadratic- a term or polynomial with the variable raised to the second power 2x23y ) Cubic a term or polynomial with the variable raised to the third power 7x3-5y ) quartic- a term or polynomial with the variable raised to the fourth power 9y4 + 4

8 5y 6y + 2 8k q2 + 9q m + 3m3 + 9m2 Linear constant Quadratic Cubic

Standard Form: terms of the polynomial are in descending order (largest degree down to the smallest degree) Ex: Write the following in standard form. Leading coefficient the coefficient of the term with the largest degree in the polynomial Identify the leading coefficient. 1.)3x2 + x )x ) 7x2 + 2x5 + 4x

Addition and Subtraction of Polynomials A: Addition (Combining Like Terms): ex 1: (-8x2 + x + 2) + ( 8x2 - 2x + 4) ex 2: (6y2 - y + 3) + ( -2y + y2 - 7)

ex 1: (-6x3 + 5x - 30) - ( 2x3 +4x2 - 3x + 1) B: Subtraction ( Distribute -1 and then combine like terms): ex 2: (12x - 8x2 + 6) - ( -8x2 - 3x + 4)