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Polynomials

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 4 - 11. What is a binomial?. A binomial is the sum of two monomials.

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Polynomials

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

  2. What is a polynomial? • A polynomial is a monomial or a sum of monomials. • Example: 7x2 + 2x4 - 11

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

  4. What is a trinomial? • A trinomial is the sum of three monomials. • Example: p2 + 5p + 4

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

  6. The degree of a monomial • To find the degree of a monomial add the exponents of all of its variables. • Example: 5mn2 has a degree of 3

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

  8. -4x2y2 + 3x2 + 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

  9. -4x2y2 + 3x2 + 5 • Therefore the degree of the polynomial is 4.

  10. Arrange polynomials in ascending order. • Arrange the terms of the polynomial so that the powers of x are in ascending order. • 7x2 + 2x4 -11 • 11 + 7x2 + 2x4

  11. 11 + 7x2 + 2x4 • 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.

  12. Arrange the polynomial in descending order. • arrange so the powers of x are in descending order. • 3a3x2 – a4 + 4ax5 + 9a2x • 4ax5 + 3a3x2 + 9a2x – a4x0

  13. 4ax5 + 3a3x2 + 9a2x – a4 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.

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