Warm Up Get out your notes and be ready to go when the bell rings! We have a lot to cover.

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Warm Up Get out your notes and be ready to go when the bell rings! We have a lot to cover.

Intro to Polynomials

Polynomials A monomial is the product of numbers, variables, or both. Ex. 5 x 6y 7jk2 A polynomial is a monomial or a group of monomials separated by + or –. Ex. 7x2 + 8xk - 4

The degree of a monomial is the sum of the exponents of the variables The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 5x2 4a4b3c -3

To find the degree of a polynomial, find the largest degree of each monomial. 1) 8x2 - 2x + 7 Degrees: 2 1 0 Which is biggest? 2 is the degree! 2) y7 + 6y4 + 3x4m4 Degrees: 7 4 8 8 is the degree!

Find the degree of x5 – x3y2 + 4 2 3 5 10

Sometimes, a polynomial will already be factored Sometimes, a polynomial will already be factored. When this is the case, add up all the exponents. Ex. (x-2)3(x+5)2(x-3)(x+7)(x+1)3

Quick Recap To find the degree of a polynomial, use the monomial with the largest degree. 7x3y + 9x2 + 4x + 5y If the polynomial is already factored, add up the exponents. (x-3)(x+4)(x-7) 3

Graphs of Polynomials The graph of a polynomial function is always a smooth curve; that is, it has no breaks or corners.