polynomials
TRANSCRIPT
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