PolynomialsPolynomials

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

What is a polynomial?What is a polynomial?

• A polynomial is a monomial or a sum of monomials.

• Example: 7x2 + 2x4 - 11

What is a binomial?What is a binomial?

• A binomial is the sum of two monomials.

• Example: 2a + 3c

What is a trinomial?What is a trinomial?

• A trinomial is the sum of three monomials.

• Example: p2 + 5p + 4

Degree of a polynomialDegree of a polynomial

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

The degree of a monomialThe degree of a monomial

• To find the degree of a monomial add the exponents of all of its variables.

• Example: 5mnExample: 5mn22 has a has a degree of 3degree of 3

Find the degree of a polynomialFind the degree of a polynomial

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

-4x-4x22yy22 + 3x + 3x2 2 + 5 + 5

• Find the degree of each term.

• -4x2y2 has a degree of 4

• 3x2 has a degree of 2

• 5 has a degree of 0

-4x-4x22yy22 + 3x + 3x2 2 + 5+ 5

• Therefore the degree of the polynomial is 4.

Arrange polynomials in ascending Arrange polynomials in ascending order.order.

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

• 7x2 + 2x4 -11

• 11 + 7x2 + 2x4

11 + 7x11 + 7x22 + 2x + 2x44

• The term 11 = 11x0

• Remember any number to the zero power is equal to one.

• Therefore, it is not necessary to have the 11x0 in the polynomial, since 11x0 = 11.

Arrange the polynomial in Arrange the polynomial in descending order.descending order.

• arrange so the powers of x are in descending order.

• 3a3x2 – a4 + 4ax5 + 9a2x• 4ax5 + 3a3x2 + 9a2x – a4x0

4ax4ax5 5 + 3a+ 3a33xx22 + 9a + 9a22x – ax – a44

Remember any number to the zero power is equal to 1.

The term a4 = a4x0 since

x0 = 1 it is not necessary to add x0 to the polynomial.