Polynomials.

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Polynomials

Unit 2: Algebra Investigation MM1A2c: Add, subtract, multiply, and divide polynomials. Essential Question: How do you add and subtract polynomials?

What does each prefix mean? mono one bi two tri three

What about the prefix: poly? MANY A polynomial is a monomial or a sum or difference of monomials. Each monomial called a term. Important Note! An expression is not a polynomial if there is a variable in the denominator.

Different Types of Polynomials Monomial: number (1, 2, 3, …), variable (a, b, c, …) or the product of a number and one or more variable (2x, -4xyz,…) Binomial: Two terms (2x + 4y, 3xz + 5) Trinomial: Three terms (4a + 2ab + 7b)

State whether each expression is a polynomial. If it is, identify it. 1) 7y - 3x + 4 trinomial 2) 10x3yz2 monomial 3) not a polynomial

Degree of a Monomial The sum of the exponents of the variables in the monomial. The degree of a nonzero constant term is 0. Ex. 4x3y2 The degree of the monomial is “5”

Find the degree of each monomial. 1) 5x2 2 4a4b3c 8 -3

Degree of a Polynomial The greatest degree of its terms. Ex. 6z3 + 7z2 – 3z7 The degree of the polynomial is “7”

Which polynomial is represented by? X 1 X 1 X2 X x2 + x + 1 x2 + x + 2 x2 + 2x + 2 x2 + 3x + 2 I’ve got no idea!

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

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

A polynomial is normally put in ascending or descending order. What is ascending order? Going from small to big exponents. What is descending order? Going from big to small exponents.

Put in descending order: 8x - 3x2 + x4 - 4 x4 - 3x2 + 8x - 4 2) Put in descending order in terms of x: 12x2y3 - 6x3y2 + 3y - 2x -6x3y2 + 12x2y3 - 2x + 3y

3) Put in ascending order in terms of y: 12x2y3 - 6x3y2 + 3y - 2x -2x + 3y - 6x3y2 + 12x2y3 Put in ascending order: 5a3 - 3 + 2a - a2 -3 + 2a - a2 + 5a3

Write in ascending order in terms of y: x4 – x3y2 + 4xy – 2x2y3 – 2x2y3 – x3y2 + 4xy + x4 x4 – x3y2– 2x2y3 + 4xy 4xy – 2x2y3 – x3y2 + x4