Polynomials A monomial is the product of numbers, variables, or both. Ex.5x6y7jk 2 A polynomial is a monomial or a group of monomials separated by + or.

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Presentation transcript:

Polynomials A monomial is the product of numbers, variables, or both. Ex.5x6y7jk 2 A polynomial is a monomial or a group of monomials separated by + or –. Ex. 7x 2 + 8xk - 4

What does each prefix mean? mono bi tri

Naming a polynomial by Terms Number of TermsName 1Monomial 2Binomial 3Trinomial 4 or more“with 4 terms” (or 5 or 6, etc.)

State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x 3 yz 2 monomial 3) not a polynomial

The degree of a monomial is the sum of the exponents of the variables. Find the degree of each monomial. 1) 5x 2 2 2)4a 4 b 3 c 8 3)-3 0

To find the degree of a polynomial, use the monomial with the highest degree. 1) 8x 2 - 2x + 7 Degrees: Which is biggest? 2 is the degree! 2) y 7 + 6y 4 + 3x 4 m 4 Degrees: is the degree!

Find the degree of x 5 – x 3 y A.0 B.2 C.3 D.5 E.10

Sometimes, a polynomial will already be factored. When this is the case, add up all the exponents. Ex. (x+1) 2 (x-3) 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. 7x 3 y + 9x 2 + 4x + 5y If the polynomial is already factored, add up the exponents. (x-3)(x+4)(x-7) 3

DegreeName 0Constant 1Linear 2Quadratic 3Cubic 4Quartic 5Quintic 6+(nth degree) Naming Polynomials by Degree

Try it! Name the following polynomials: x 3 x 5 – xy + 3y 2 t 2 – 8 j 4 + 6jk – 3j + 2

Adding and Subtracting Polynomials Combine like terms. Watch out for degrees! Don’t combine x and x 2. When subtracting, be sure to distribute the negative to all terms.

Example 1: Add the following polynomials: (9y - 7x + 15a) + (-3y + 8x - 8a) Example 2: Add the following polynomials: (3a 2 + 3ab - b 2 ) + (4ab + 6b 2 )

Example 3: Add the following polynomials: (4x 2 - 2xy + 3y 2 ) + (-3x 2 - xy + 2y 2 ) Example 4: Subtract the following polynomials: (9y - 7x + 15a) - (-3y + 8x - 8a)

Example 5: Subtract the following polynomials: (7a - 10b) - (3a + 4b) Example 6: Subtract the following polynomials: (4x 2 - 2xy + 3y 2 ) - (-3x 2 - xy + 2y 2 )

Find the sum or difference. (5a – 3b) + (2a + 6b) A.3a – 9b B.3a + 3b C.7a + 3b D.7a – 3b

Find the sum or difference. (5a – 3b) – (2a + 6b) A.3a – 9b B.3a + 3b C.7a + 3b D.7a – 9b

Homework – Day 1 and by degree.