POLYNOMIALS

JOURNAL ENTRY:DESCRIBE THE RULES FOR THE FOLLWOING

Power of a Power Property: Power of a Product

Property: Power of Quotient:

MULTIPLYING MONOMIALS

(-2x4y2) (-3xy2z3) = (-2)(-3)(x4x )(y2y2 ) z3

6x5y4 z3

(-2x3y4) 2 (-3xy2) (-2 ) 2 x3∙2y4∙2 ) (-3xy2) (4)(-3)(x6x) (y8 y2 ) -12x7y10

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

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.

TELL WHETHER EACH EXPRESSION IS A POLYNOMIAL AND STATE WHAT KIND.

4x + 9x +4 Trinomial xy + 3xy³ Binomial

IDENTIFY THE TERMS AND GIVE THE COEFFICIENT OF EACH TERM

4x³y² - 3z² + 5 Term 4x³y² has a coefficient of 4 Term -3xz² has a coefficient of -3 Term 5 has a coefficient of 5

COLLECTING LIKE TERMS

2x²y³ + 3x³y² - 4x²y³ + 6x³y²

2x²y³ + - 4xy + 3x³y² - 4x²y³ - 8xy + 6x³y²

IDENTIFY THE DEGREE OF A POLYNOMIAL

The degree of a term is the sum of the exponents of the variables. The degree of a polynomial 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.

IDENTIFY THE DEGREE OF EACH TERM AND THE DEGREE OF THE POLYNOMIAL

2xy³ + 3x³y - 4x²y³

2x²y³ + - 4xy + 3xy² - 4x²y²

DESCENDING ORDER

The polynomial 3x3y4+2x2y3-xy5-7 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 -xy5 +2x2y3+ 3x3y4 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.

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

4a3 + 7a2b + b3 - 3ab2 + b3 - a3 + 3a2b