The document defines and provides examples of polynomials, monomials, binomials, trinomials, terms, coefficients, degrees of terms and polynomials, collecting like terms, and arranging polynomials in descending and ascending order. Specifically: - A polynomial is a sum of monomials, with each monomial being a term. - A monomial is a number, variable, or product of numbers and variables with whole number exponents. - Binomials have two terms, trinomials have three terms. - The coefficient is the numeric factor of a term. - The degree of a term is the sum of its variable exponents, and the degree of a polynomial is the highest term degree.

1. POLYNOMIALS

2. JOURNAL ENTRY: DESCRIBE THE RULES FOR THE FOLLWOING Power of a Power Property : Power of a Product Property : Power of Quotient:

3. MULTIPLYING MONOMIALS (-2x 4 y 2 ) (-3xy 2 z 3 ) = (-2)(-3)(x 4 x )(y 2 y 2 ) z 3 6x 5 y 4 z 3 (-2x 3 y 4 ) 2 (-3xy 2 ) (-2 ) 2 x 3∙2 y 4∙2 ) (-3xy 2 ) (4)(-3)(x 6 x) (y 8 y 2 ) -12x 7 y 10

5. MULTIPLYING AND DIVIDING MONOMIALS Monomial – an expression that is either a numeral, a variable or a product of numerals and variables with whole number exponents. Constant – Monomial that is a numeral. Example - 2

6. POLYNOMIALS Polynomial – a monomial or a sum of monomials. Each monomial in a polynomial is referred to as a term Special types of Polynomials Monomial – an expression that is a number, a variable, or a product of numbers and or variables Binomial – a polynomial with exactly two terms. Trinomials – a polynomial with exactly three terms. Coefficient – The numeric factor of a term.

7. TELL WHETHER EACH EXPRESSION IS A POLYNOMIAL AND STATE WHAT KIND. 4x + 9x +4 Trinomial xy + 3xy³ Binomial

8. IDENTIFY THE TERMS AND GIVE THE COEFFICIENT OF EACH TERM 4x³y² - 3z² + 5 Term 4x³y² has a coefficient of 4 Term -3xz² has a coefficient of -3 Term 5 has a coefficient of 5

9. COLLECTING LIKE TERMS 2x²y³ + 3x³y² - 4x²y³ + 6x³y² 2x²y³ + - 4xy + 3x³y² - 4x²y³ - 8xy + 6x³y²

10. IDENTIFY THE DEGREE OF A POLYNOMIAL The degree of a term is the sum of the exponents of the variables . The degree of a polynomia l is the highest degree of its terms. Example: 3a²b³ + 3x³y³ + 2 The degree of 3a²b³ is 5 The degree of 3x³y³ is 6 The degree of 2 is 0 The term with the highest degree is called the leading term.. The coefficient of the leading term is called the leading coefficient.

11. IDENTIFY THE DEGREE OF EACH TERM AND THE DEGREE OF THE POLYNOMIAL 2xy³ + 3x³y - 4x²y³ 2x²y³ + - 4xy + 3xy² - 4x²y²

12. DESCENDING ORDER The polynomial 3x 3 y 4 +2x 2 y 3 -xy 5 -7 is written in descending order for the variable x. The term with the greatest exponent for x is first, the term with the next greatest exponent for x is second and so on. The polynomial 7 -xy 5 +2x 2 y 3 + 3x 3 y 4 is written in ascending order for the variable x. The term with the least exponent for x is first, the term with the next larger exponent for x is second and so on.

13. Collect like terms and Arrange each polynomial in descending order for x 3x²y³ + - 2xy + 3x³y² - 5x²y³ - 8xy + 4x³y² 7x³y² - 2x²y³ -10xy Collect like terms and Arrange each polynomial in descending order for b 4a 3 + 7a 2 b + b 3 - 3ab 2 + b 3 - a 3 + 3a 2 b