polynomials
TRANSCRIPT
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POLYNOMIALS
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JOURNAL ENTRY:DESCRIBE THE RULES FOR THE FOLLWOING
Power of a Power Property: Power of a Product
Property: Power of Quotient:
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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
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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
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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.
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TELL WHETHER EACH EXPRESSION IS A POLYNOMIAL AND STATE WHAT KIND.
4x + 9x +4 Trinomial xy + 3xy³ Binomial
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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
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COLLECTING LIKE TERMS
2x²y³ + 3x³y² - 4x²y³ + 6x³y²
2x²y³ + - 4xy + 3x³y² - 4x²y³ - 8xy + 6x³y²
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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.
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IDENTIFY THE DEGREE OF EACH TERM AND THE DEGREE OF THE POLYNOMIAL
2xy³ + 3x³y - 4x²y³
2x²y³ + - 4xy + 3xy² - 4x²y²
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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.
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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