"In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables."
Polynomials are expressions that contain multiple terms with coefficients and variables raised to various powers.
Algebraic Expressions: An expression containing variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division.
Polynomials: An algebraic expression in which the variables are raised to powers and multiplied by coefficients.
Degree of a polynomial: The highest power of the variable in a polynomial.
Monomials: Polynomials consisting of a single term.
Binomials: Polynomials consisting of two terms.
Trinomials: Polynomials consisting of three terms.
Adding and subtracting polynomials: Combining like terms in polynomials.
Multiplying polynomials: Multiplying two polynomials to obtain a third polynomial.
Factoring polynomials: Expressing a polynomial as a product of simpler polynomials or factors.
The zero factor property: If the product of two factors is zero, then at least one of the factors must be zero.
Solving equations using polynomials: Using algebraic manipulations to solve equations that involve polynomials.
Synthetic division: A method for dividing polynomials quickly and easily.
Rational functions: A ratio of two polynomials.
Finding roots of polynomials: Solving equations of the form f(x) = 0, where f(x) is a polynomial.
Descartes' rule of signs: A method for determining the real roots of a polynomial based on the signs of its coefficients.
Cubic polynomial: :.
"An example of a polynomial of a single indeterminate x is x2 − 4x + 7."
"Yes, an example with three indeterminates is x3 + 2xyz2 − yz + 1."
"Polynomials appear in many areas of mathematics and science."
"They are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems."
"They are used to define polynomial functions, which appear in settings ranging from basic chemistry and physics to economics and social science."
"They are used in calculus and numerical analysis to approximate other functions."
"In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry."
"Indeterminates (also called variables)."
"The operations involved in a polynomial are addition, subtraction, multiplication, and positive-integer powers of variables."
"An example of a polynomial equation is x2 − 4x + 7 = 0."
"Polynomial functions appear in settings ranging from basic chemistry and physics to economics and social science."
"The operations of addition, subtraction, multiplication, and positive-integer powers of variables are the only operations involved in polynomials."
"Polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry."
"Yes, polynomials are used to encode a wide range of problems, from elementary word problems to complicated scientific problems."
"Yes, polynomials are used in calculus and numerical analysis to approximate other functions."
"A polynomial can have any number of indeterminates, such as three indeterminates in the example x3 + 2xyz2 − yz + 1."
"Polynomials are used to form polynomial equations, which encode a wide range of problems, from elementary word problems to complicated scientific problems."
"Polynomials are used to construct polynomial rings and algebraic varieties, which are central concepts in algebra and algebraic geometry."
"Yes, polynomials are used to define polynomial functions in multiple fields, ranging from basic chemistry and physics to economics and social science."