Polynomial functions
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Polynomial functions are algebraic expressions involving powers of variables with coefficients. This document discusses polynomial functions and their different forms, including standard form which lists terms in descending order by exponent, and factored form which groups the terms by their factors. Key vocabulary includes degree, which refers to the highest power in the expression, and leading coefficient, the coefficient of the first term. Examples of polynomial functions in standard form are provided.
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Polynomial functions
This document discusses polynomial functions and provides examples and definitions of key terms. It defines a polynomial function as one where all terms are combined using addition, subtraction, and multiplication, and all terms have a non-negative integer exponent. Examples given are F(x)=6x^4-3x^2+2x-5 and F(x)=x-2+5, with the latter noted as not a polynomial. Key terms defined include degree, leading coefficient, standard form, and factored form.
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- An algebraic expression involving variables with only non-negative integer powers is called a polynomial. The highest power of the variable in a polynomial is called its degree.
- Polynomials can be classified by their degree and number of terms. For example, a polynomial of degree 2 with 3 terms is called a trinomial.
- Common algebraic identities involving polynomials include factoring expressions like (a+b)2, (a-b)2, and a2-b2. Polynomials can also be factored using the difference of squares or sum/difference of cubes identities.
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The document discusses the Alexander polynomial, which is a knot invariant that assigns an integer polynomial to each knot type. It was discovered in 1923 by James Waddell Alexander II as the first knot polynomial. In 1969, John Conway showed that a version of this polynomial, now called the Alexander-Conway polynomial, could be computed using a skein relation. Soon after, it was realized that Alexander's original paper also exhibited a similar skein relation for his polynomial.
Ch.11.1 Adding and Subtracting Polynomials
This document provides an overview of adding and subtracting polynomials:
- It defines polynomials as algebraic expressions made up of terms that are added or subtracted. The degree is the highest power of the variable.
- Polynomials should be written in standard form with terms in descending order of power.
- Like terms are those with the same variables and powers, while unlike terms do not match.
- To simplify a polynomial, combine all like terms.
- Examples are provided for adding and subtracting polynomials by combining like terms.
Polynomials
The document defines and provides examples of polynomials. It states that a polynomial is an expression that can include constants, variables, and exponents, and can be combined using addition, subtraction, multiplication, and division, as long as it does not involve dividing by a variable or having fractional exponents. The document then gives examples of polynomials and non-polynomials. It also discusses key properties of polynomials including their degree, standard form, adding and subtracting polynomials, and finding zeros of polynomials.
IX polynomial
All the best to all students of class IX...This PPT will makes your difficulties easy to do....You will understand the polynomial chapter easily by seeing this ....Thanks for watching this ..Please Share, Like and Subscribe the PPT
Polynomials
The document defines and provides examples of various algebraic expressions including monomials, binomials, trinomials, and polynomials. It explains that a polynomial is an algebraic expression with variables that have only non-negative integral powers. The degree of a polynomial refers to the highest power of the variable. Quadratic polynomials specifically are polynomials of degree 2. The document also discusses finding zeros of polynomials and provides examples of factoring polynomials using common identities.
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This document provides an overview of polynomials. It defines polynomials as expressions with multiple terms where the exponents are whole numbers. Monomials have one term, binomials have two terms, and trinomials have three terms. Polynomials can have variables, constants, and exponents of whole numbers. Expressions with non-whole number exponents or fractions are not polynomials. The document also notes that polynomials of one variable can be written as a sum of terms with coefficients and descending exponents, and the highest exponent indicates the degree of the polynomial.
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Polynomial functions
This document discusses polynomial functions and provides examples and definitions of key terms. It defines a polynomial function as one where all terms are combined using addition, subtraction, and multiplication, and all terms have a non-negative integer exponent. Examples given are F(x)=6x^4-3x^2+2x-5 and F(x)=x-2+5, with the latter noted as not a polynomial. Key terms defined include degree, leading coefficient, standard form, and factored form.
Math ppt copy (2)
- An algebraic expression involving variables with only non-negative integer powers is called a polynomial. The highest power of the variable in a polynomial is called its degree.
- Polynomials can be classified by their degree and number of terms. For example, a polynomial of degree 2 with 3 terms is called a trinomial.
- Common algebraic identities involving polynomials include factoring expressions like (a+b)2, (a-b)2, and a2-b2. Polynomials can also be factored using the difference of squares or sum/difference of cubes identities.
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The document discusses the Alexander polynomial, which is a knot invariant that assigns an integer polynomial to each knot type. It was discovered in 1923 by James Waddell Alexander II as the first knot polynomial. In 1969, John Conway showed that a version of this polynomial, now called the Alexander-Conway polynomial, could be computed using a skein relation. Soon after, it was realized that Alexander's original paper also exhibited a similar skein relation for his polynomial.
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This document provides an overview of adding and subtracting polynomials:
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- Like terms are those with the same variables and powers, while unlike terms do not match.
- To simplify a polynomial, combine all like terms.
- Examples are provided for adding and subtracting polynomials by combining like terms.
Polynomials
The document defines and provides examples of polynomials. It states that a polynomial is an expression that can include constants, variables, and exponents, and can be combined using addition, subtraction, multiplication, and division, as long as it does not involve dividing by a variable or having fractional exponents. The document then gives examples of polynomials and non-polynomials. It also discusses key properties of polynomials including their degree, standard form, adding and subtracting polynomials, and finding zeros of polynomials.
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The document defines and provides examples of various algebraic expressions including monomials, binomials, trinomials, and polynomials. It explains that a polynomial is an algebraic expression with variables that have only non-negative integral powers. The degree of a polynomial refers to the highest power of the variable. Quadratic polynomials specifically are polynomials of degree 2. The document also discusses finding zeros of polynomials and provides examples of factoring polynomials using common identities.
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This document provides an overview of polynomials. It defines polynomials as expressions with multiple terms where the exponents are whole numbers. Monomials have one term, binomials have two terms, and trinomials have three terms. Polynomials can have variables, constants, and exponents of whole numbers. Expressions with non-whole number exponents or fractions are not polynomials. The document also notes that polynomials of one variable can be written as a sum of terms with coefficients and descending exponents, and the highest exponent indicates the degree of the polynomial.
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The document provides information about polynomials including:
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Polynomial functions
- 1. Polynomial Functions BY: Amanda Duncan
- 2. EXAMPLES OF FUNCTIONS 6x^4-3x^2+2x 7x^5-3x^2-8x X^12
- 3. Vocabulary Degree– highest power of X in standard form Leading Coefficient– the coefficient of the first term when the terms are in descending order
- 4. Different forms Standard form— F(X)= Ax^n+Bx^n+Cx+H Factored Form— (X-R1)(X+R2)(X-R3)