Classifying Polynomials

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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.

The prefix “mono” means 1 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?

The prefix “quad” means 4 Quadnomial: four terms (separated by + or -) The prefix “quad” means 4 Can you name a quadnomial?

The prefix “poly” means MANY Polynomial: a monomial or a sum of monomials. (separated by + or -) Many terms. The prefix “poly” means MANY Can you name a polynomial?

1/80z3 2. a8 – 1/5a + 2a 3. 2x + 6z 4. 4st3 + 1.2t2 – 0.8st Monomial Determine the name of the polynomial. 1/80z3 2. a8 – 1/5a + 2a 3. 2x + 6z 4. 4st3 + 1.2t2 – 0.8st Monomial Trinomial Binomial Trinomial

6) 5) Monomial Quadnomial 7) Polynomial Determine the name of the polynomial. 6) 5) Quadnomial Monomial 7) Polynomial

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!

2 + x4 + x2 6x – 3x2 + 4 – 2x8 x4 + x2 + 2 – 2x8 – 3x2 + 6x + 4 Rewrite the following in descending order. 2 + x4 + x2 6x – 3x2 + 4 – 2x8 x4 + x2 + 2 – 2x8 – 3x2 + 6x + 4 3. 7x6 + x2 + 24 – x3 7x6 – x3 + x2 +24

2x4 + 3x Remember: A coefficient is a number in front of a variable.

A leading coefficient is the coefficient of the FIRST TERM when the polynomial is written in descending order (standard form). 2x3 + 4x + 5 Leading coefficient

Leading coefficient = -1 -x5 + x4 + 2x +4; Write the polynomial in descending order (standard form). Then name the leading coefficient. 4. Leading coefficient = 2 2x2 + 3x - 1; 5. Leading coefficient = -1 -x5 + x4 + 2x +4; 6. Leading coefficient = 4 4x3 + x2 + 2x – 7 ;