Polynomials Objective: find the degree of a polynomial. Arrange the terms of a polynomial in ascending or descending order.

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Presentation transcript:

Polynomials Objective: find the degree of a polynomial. Arrange the terms of a polynomial in ascending or descending order.

What is a polynomial? A polynomial is a monomial or a sum of monomials. Example: 7x 2 + 2x

What is a binomial? A binomial is the sum of two monomials. Example: 2a + 3c

What is a trinomial? A trinomial is the sum of three monomials. Example: p 2 + 5p + 4

Degree of a polynomial The degree of a polynomial is the greatest degree of any term in the polynomial.

The degree of a monomial To find the degree of a monomial add the exponents of all of its variables. Example: 5mn 2 has a degree of 3

Find the degree of a polynomial To find the degree of a polynomial you must find the degree of each monomial in the polynomial.

-4x 2 y 2 + 3x Find the degree of each term. -4x 2 y 2 has a degree of 4 3x 2 has a degree of 2 5 has a degree of 0

-4x 2 y 2 + 3x Therefore the degree of the polynomial is 4.

Arrange polynomials in ascending order. Arrange the terms of the polynomial so that the powers of x are in ascending order. 7x 2 + 2x x 2 + 2x 4

The term 11 = 11x 0 Remember any number to the zero power is equal to one. Therefore, it is not necessary to have the 11x 0 in the polynomial, since 11x 0 = 11.

Arrange the polynomial in descending order. arrange so the powers of x are in descending order. 3a 3 x 2 – a 4 + 4ax 5 + 9a 2 x 4ax 5 + 3a 3 x 2 + 9a 2 x – a 4 x 0

4ax 5 + 3a 3 x 2 + 9a 2 x – a 4 Remember any number to the zero power is equal to 1. The term a 4 = a 4 x 0 since x 0 = 1 it is not necessary to add x 0 to the polynomial.