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A polynomial function consists of either zero or the sum of a finite number of non-zero terms, each of which is a product of a number, also known as the coefficient of a term, and a variable raised to a non-negative integer power

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Descartes' rule of signs describes the relationship between the number of sign changes in f(x) and the number of positive real zeros

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The linear factorization theorem shows us that a polynomial function will have the same number of factors as its degree, and that each factor will be in the form of (x-c), the c being the constant

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The fundamental theorem of algebra teaches us that every polynomial function has at least one complex zero

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Rational zero theorem can be utilized in order to narrow down possible rational using the ratio of the factors of the constant term and factors of the leading coefficient of the polynomial

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The remainder theorem tells us that if f(x) is a polynomial in x, the remainder on dividing f(x) by x, then - a is f(a)

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The division algorithm tells us that with a polynomial dividend and a non-zero polynomial divisor, where the degree of the divisor is less than or equal to the degree of the dividend, there exists unique polynomials (the quotient and the remainder).

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Synthetic division is the shorthand version of dividing a polynomial that is done with a function who's leading coefficient is 1.

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The minimum value of a quadratic function is how we describe the lowest point at which a a vertex of a function reaches

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The maximum value of a quadratic function is what describes the highest point that the vertex of a graph reaches

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The axis of symmetry is a line that we can draw through a function's vertex, dividing it directly down the middle

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The phrase "finding the zeros" is referencing finding the x-intercepts of the equation (where the value of y=0)

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The turning point is a term that we use to describe the point at which a function changes from decreasing to increasing, or visa versa

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The leading term is the term which contains either the highest power of a variable, or the term with the highest degree

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The leading coefficient is..... you guessed it! The coefficient of the leading term

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The degree of a polynomial is defined as the highest value variable that occurs in a function, which belongs to the first variable (if the equation is in general form)

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The end behavior is how we describe where the left end of the function is pointing and where the right end of the function is pointing or "ending" on the graph. This gives us information about what a graphs equation might look like, if it is not provided.

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A power function can be defined as a function with a term that is the product of a real number, a coefficient, as well as a variable raised to a fixed real number.
An example of a power function is the area of a circle

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The vertex of a quadratic function is written as
f(x)=a(x-h)²+k
Also known as standard form, this can tell us the coordinates of the vertex

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The general form of a quadratic function is written as
f(x)=a x ²+b x+c
And we are able to use this form in order to determine the equation for the line of symmetry