9-4 Polynomials

9-4 Polynomials

Classifying Polynomials What you WILL Learn: 1) To find the degree of a polynomial 2) To arrange the terms of a polynomial so that the powers of a variable are in ascending or descending order. Monomial: one term (no + or -) The prefix

mono means 1 Can you name a monomial? Binomial: two terms (separated by + or -) The prefix bi means 2 Can you name a binomial?

Trinomial: three terms (separated by + or -) The prefix tri means 3 Can you name a trinomial? Quadnomial: four terms (separated by + or -) The prefix quad means

4 Can you name a quadnomial? Polynomial: a monomial or a sum of monomials. (separated by + or -) Many terms. Can you name a polynomial? The prefix

poly means MANY Determine the name of the polynomial. 1.1/80z3 Monomial 3. 2x + 6z

Binomial 2. a8 1/5a + 2a Trinomial 3 2 4. 4st + 1.2t

Trinomial 0.8st Determine the name of the polynomial. 6) 5) Quadnomial 7) Polynomial

Monomial DESCENDING: means decreasing. Going from big to small. Descending Order: Exponents go from BIG TO SMALL! *Numbers always go last because they have a degree of zero. Example: 3x2 + 7x + 5

Descending order is often referred to as standard form. You should always write your answers in standard form! Rewrite the following in descending order. 1. 2 + x4 + x2 x4 + x2 + 2

2. 6x 3x2 + 4 2x8 2x8 3x2 + 6x + 4 3. 7x6 + x2 + 24 x3 7x6 x3 + x2 +24 Remember: A coefficient is a number in front of a variable.

2x + 3x 4 Coefficient A leading coefficient is the coefficient of the FIRST TERM when the polynomial is written in descending order (standard form).

2x + 4x + 5 3 Leading coefficient Write the polynomial in descending order (standard form). Then name the leading coefficient. 4.

1 3x 2 x 2 Leading coefficient = 2 2x2 + 3x - 1; 5. -x5 + x4 + 2x +4;

Leading coefficient = -1 6. 4x3 + x2 + 2x 7 ; Leading coefficient = 4

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