Enhance Your Learning with Polynomials and Factoring Flash Cards for quick understanding
An algebraic expression consisting of variables, coefficients, and exponents, combined using addition, subtraction, multiplication, and non-negative integer exponents.
The highest exponent of the variable in a polynomial. It determines the complexity and behavior of the polynomial.
The numerical factor of a term in a polynomial. It is multiplied by the variable(s) and exponent(s).
A polynomial with only one term. It can be a constant, a variable, or a product of constants and variables.
A polynomial with two terms. It can be a sum or difference of two monomials.
A polynomial with three terms. It can be a sum or difference of three monomials.
The process of combining like terms in polynomials by adding their coefficients.
The process of combining like terms in polynomials by subtracting their coefficients.
The process of multiplying the coefficients and adding the exponents of variables when multiplying monomials.
The process of multiplying each term of one polynomial by each term of another polynomial and combining like terms.
The process of expressing a polynomial as a product of its factors. It helps in simplifying and solving polynomial equations.
The largest factor that divides evenly into two or more terms. It is used to factor out common terms from a polynomial.
The process of grouping terms in a polynomial and factoring out the greatest common factor from each group.
The process of factoring trinomials of the form ax^2 + bx + c, where a ≠ 0, by finding two binomials whose product is the trinomial.
The process of factoring trinomials of the form a^2 + 2ab + b^2 or a^2 - 2ab + b^2, where a and b are constants.
The process of factoring expressions of the form a^2 - b^2, where a and b are constants.
The process of factoring expressions of the form a^3 ± b^3, where a and b are constants.
A theorem that helps in finding rational roots (zeros) of a polynomial equation by considering the factors of the constant term and the leading coefficient.
A method used to divide a polynomial by a linear binomial of the form (x - c), where c is a constant.
A method used to divide a polynomial by another polynomial of higher degree, similar to long division of numbers.
An equation of the form ax^2 + bx + c = 0, where a ≠ 0. It can be solved using factoring, completing the square, or the quadratic formula.
A method used to solve quadratic equations by adding a constant term to both sides of the equation to create a perfect square trinomial.
The expression b^2 - 4ac in the quadratic formula. It determines the nature of the roots (real, imaginary, or equal) of a quadratic equation.
The values of x that satisfy a quadratic equation. They can be real, imaginary, or equal depending on the discriminant.
A form of a quadratic equation given by y = a(x - h)^2 + k, where (h, k) represents the vertex of the parabola.
A form of a quadratic equation given by ax^2 + bx + c = 0, where a, b, and c are constants and a ≠ 0.
The process of plotting points and sketching the graph of a quadratic equation, which forms a parabola.
The behavior of the graph of a polynomial as x approaches positive or negative infinity. It is determined by the degree and leading coefficient of the polynomial.
The values of x that make a polynomial equal to zero. They can be real or complex.
A theorem that states that every polynomial equation of degree n has exactly n complex roots, counting multiplicities.
A rule that helps in determining the possible number of positive and negative real roots of a polynomial equation by examining the signs of its coefficients.
The range of possible values for the roots of a polynomial equation, determined by the rational root theorem and Descartes' rule of signs.
Inequalities involving polynomials, where the goal is to find the values of x that satisfy the inequality.
A way to represent the solution set of an inequality using intervals on the number line.
Inequalities involving absolute value expressions, where the goal is to find the values of x that satisfy the inequality.
Functions defined by different rules or formulas for different intervals or subdomains of the input variable.
Real-world problems and scenarios that can be modeled and solved using polynomial equations and functions.
A statistical method used to fit a polynomial function to a set of data points, allowing for curve fitting and prediction.
Problems that involve finding the maximum or minimum value of a quantity, often modeled using polynomial functions.
The relationship between the roots (zeros) and factors of a polynomial equation, where the roots are the x-intercepts of the graph and the factors are the linear expressions.
Numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit (√(-1)). They are used to represent solutions to equations with no real roots.
Pairs of complex numbers of the form a + bi and a - bi, where a and b are real numbers. They have the same real part and opposite imaginary parts.
The process of dividing a polynomial by another polynomial to find the quotient and remainder.
The process of decomposing a rational function into simpler fractions, often used in integration and solving differential equations.
Functions defined by polynomial equations, where the input variable is raised to non-negative integer powers and multiplied by coefficients.
The behavior of the graph of a polynomial function as x approaches positive or negative infinity. It is determined by the degree and leading coefficient of the polynomial.
Points on the graph of a polynomial function where the direction of the graph changes from increasing to decreasing or vice versa.
Points on the graph of a polynomial function where the function reaches a maximum or minimum value within a specific interval.
The property of a polynomial function where the graph exhibits symmetry with respect to the y-axis, x-axis, or origin.
The behavior of the graph of a polynomial function as x approaches positive or negative infinity. It is determined by the degree and leading coefficient of the polynomial.
The process of plotting points and sketching the graph of a polynomial function, which exhibits various behaviors based on its degree and leading coefficient.