6-1 Polynomial Functions Classifying polynomials

Classifying a polynomial – Standard form First classify the polynomial by exponents Descending order for exponents (with one variable) – Largest exponent to smallest exponent – When writing a polynomial in standard form first combine like terms then rewrite the polynomial in descending order Then classify the polynomial by the number of terms – Monomial » One term – Binomial » Two terms – Trinomial » Three terms – Polynomial » Anything more than three terms

Degree of a polynomial Largest degree of any term of the polynomial – Constant7degree = 0 – Linearx + 3degree = 1 – Quadratic7x 2 degree = 2 – Cubic3x 3 - 5x 2 + 2x – 5 degree = 3 – The degree of a polynomial is different from number of terms --- In the above examples the quadratic has one term and the cubic has 4 terms

We classify polynomials according to the degree of the polynomial and then the number of terms. 3x 3 - 5x 2 + 2x – 5, is a polynomial of degree 3 and number of terms 4 or more formally a cubic polynomial 7x 2 has a degree of two and only one term so it is a quadratic monomial

6-2 Polynomials and Linear Functions

Writing a polynomial in standard form from factored form – Multiply all terms, combine like terms and rewrite the polynomial in standard form Descending order – Largest exponent to smallest exponent – Example (x+3)(x+4)(x-2)(x) Multiply all terms Combine like terms Rewrite the polynomial in descending order

Factoring a polynomial from standard form – Factor out the greatest common factor – Factor the remaining terms Example Factor GCF Factor remaining terms Check your work by multiplying factors and combining like terms and rewriting the polynomial in descending order

Homework: p. 309: 1 – 12; p. 317: 1 – 12