Lesson 8-4 Polynomials. Definitions Polynomial- a monomial or a sum of monomials. Binomial- the sum of two monomials. Trinomial- the sum of three monomials.

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Lesson 8-4 Polynomials

Definitions Polynomial- a monomial or a sum of monomials. Binomial- the sum of two monomials. Trinomial- the sum of three monomials.

State whether each expression is a polynomial. If it is a polynomial, identify it as a monomial, binomial, or trinomial.

Write a Polynomial Ex. 2 Write a polynomial for the area of the shaded region. r b A = b(2r) - ∏r 2 A = 2br - ∏r 2

Write a Polynomial Write a polynomial for the area of the shaded region. b h h

Degree of a monomial- the sum of the exponents of all its variables. Degree of a polynomial- the greatest degree of any term in the polynomial.

Find the degree of each polynomial.

Arrange Polynomials in Ascending Order Ex. 4 Arrange the terms of each polynomial so that the powers of x are in ascending order. 7x 2 + 2x The terms of a polynomial are usually arranged so that the powers of one variable are in ascending (increasing) order or descending (decreasing) order. 2xy 3 + y 2 + 5x 3 - 3x 2 y

Arrange the terms of each polynomial so that the powers of x are in ascending order.

Arrange Polynomials in Descending Order Ex. 5 Arrange the terms of each polynomial so that the powers of x are in descending order. 6x x -2x 3 3a 3 x 2 - a 4 + 4ax 5 + 9a 2 x

Arrange the terms of each polynomial so that the powers of x are in descending order x xy 3 - 4x 3 y a 4 + ax 2 -2a 3 xy 3 - 9x 4 y