Classifying Polynomials 7-6 Classifying Polynomials What you WILL Learn: 1) To find the degree of a polynomial 2) To arrange the terms of a polynomial so that the powers of a variable are in ascending or descending order.

The prefix “mono” means 1 7-6 Monomial: one term (no + or -) The prefix “mono” means 1 Can you name a monomial?

Binomial: two terms (separated by + or -) 7-6 The prefix “bi” means 2 Can you name a binomial?

Trinomial: three terms (separated by + or -) 7-6 Trinomial: three terms (separated by + or -) The prefix “tri” means 3 Can you name a trinomial?

The prefix “quad” means 4 7-6 Quadnomial: four terms (separated by + or -) The prefix “quad” means 4 Can you name a quadnomial?

The prefix “poly” means MANY 7-6 Polynomial: a monomial or a sum of monomials. (separated by + or -) The prefix “poly” means MANY Can you name a polynomial?

1/80z3 2. a8 – 1/5a + 2a 3. 2x + 6z 4. 4st3 + 1.2t2 – 0.8st Monomial 7-6 Determine the name of the polynomial. 1/80z3 2. a8 – 1/5a + 2a 3. 2x + 6z 4. 4st3 + 1.2t2 – 0.8st Monomial Trinomial Binomial Trinomial

6) 5) Monomial Quadnomial 7) Polynomial 7-6 Determine the name of the polynomial. 6) 5) Quadnomial Monomial 7) Polynomial

The degree of a MONOMIAL: the sum of the exponents of its variables. 7-6 The degree of a MONOMIAL: the sum of the exponents of its variables. Example: The degree of 5a2bc5 would be 8. 1 (2+1+5 = 8)

The degree of 2x2 + 9x3 + 4x5 would be 5. 7-6 The degree of a BINOMIAL, TRINOMIAL, QUADNOMIAL, or POLYNOMIAL: the GREATEST degree of all monomials in the polynomial. Example: The degree of 2x2 + 9x3 + 4x5 would be 5.

Next we are going to discuss the DEGREE. 7-6 Next we are going to discuss the DEGREE. The degree helps us put things in order. Think about where the degree symbol is for temperature… 71°… The degree symbol is in the exponent spot When finding the degree, look at the exponent

Find the degree of the monomial or polynomial. 7-6 Find the degree of the monomial or polynomial. 7 5. d8 + h9 9 3 6. x8 + y9 – z10 +a4 10 11 7. a8 + 9a – 12a9 9 7

Find the degree of the monomial or polynomial. 7-6 Find the degree of the monomial or polynomial. 8. a8 + 9a2 + a6 8 9. 2x3 3 10. 7w5 + 2w +w4 5

The degree of a number is always zero! 7-6 The degree of a number is always zero! The degree of 12 = 0 The degree of 3 = 0 The degree of -2 = 0

Linear means x Quadratic means x2 Cubic means x3 Quartic means x4 We also classify the polynomials based on the degree. Linear means x Quadratic means x2 Cubic means x3 Quartic means x4

ASCENDING: means increasing. 7-6 ASCENDING: means increasing. If you are asked to put a polynomial in ascending order that means: Exponents go from SMALL TO BIG! Example: 5 + 7x + 3x2

DESCENDING: means decreasing. Going from big to small. 7-6 DESCENDING: means decreasing. Going from big to small. Descending Order: Exponents go from BIG TO SMALL! *Numbers always go last because they have a degree of zero. Example: 3x2 + 7x + 5

Descending order is often referred to as standard form. You should always write your answers in standard form!

2 + x4 + x2 6x – 3x2 + 4 – 2x8 x4 + x2 + 2 – 2x8 – 3x2 + 6x + 4 7-6 Rewrite the following in descending order. 2 + x4 + x2 6x – 3x2 + 4 – 2x8 x4 + x2 + 2 – 2x8 – 3x2 + 6x + 4 13. 7x6 + x2 + 24 – x3 7x6 – x3 + x2 +24

2x4 + 3x Remember: A coefficient is a number in front of a variable. 7-6 Remember: A coefficient is a number in front of a variable. 2x4 + 3x Coefficient

7-6 A leading coefficient is the coefficient of the FIRST TERM when the polynomial is written in descending order (standard form). 2x3 + 4x + 5 Leading coefficient

Leading coefficient = -1 -x5 + x4 + 2x +4; 7-6 Write the polynomial in descending order (standard form). Then name the leading coefficient. 16. Leading coefficient = 2 2x2 + 3x - 1; 17. Leading coefficient = -1 -x5 + x4 + 2x +4; 18. Leading coefficient = 4 4x3 + x2 + 2x – 7 ;