Polynomial Functions | Don't Memorise

TL;DR

Polynomial functions are functions that involve a variable raised to non-negative integral powers, and their terms are written in descending order of power.

Transcript

what is the polynomial function it is a function of the form f of X is equal to n multiplied by X raise to n plus a and minus 1 multiplied by X raise to n minus 1 and so on up to a 0 we will begin by making a few observations so how many variables do we see here we see only one variable X so we can say f of X is a function in X we notice that X ter... Read More

Key Insights

• ✊ A polynomial function involves one variable raised to unique powers, with real coefficients.
• ✊ The terms of a polynomial function can be written in ascending or descending powers of the variable.
• 🍉 The degree of a polynomial function is determined by the highest power of the variable term, unless the coefficient of that term is zero.
• 🥺 The leading coefficient of a polynomial function is the coefficient of the variable term with the highest power.
• 🍉 The terms with powers of 0, 1, and 2 in a polynomial function are called constant, linear, and quadratic terms, respectively.
• 🍉 The absence of certain terms in a polynomial function does not invalidate its status as a polynomial function, as long as the highest power term is present.
• ✊ Functions with variable terms raised to fractional or negative powers are not considered polynomial functions.

Questions & Answers

Q: What is a polynomial function?

A polynomial function is a function that involves a variable raised to non-negative integral powers, with real coefficients.

Q: What is the standard form of a polynomial function?

The standard form of a polynomial function is when its terms are written in descending order of power.

Q: How is the degree of a polynomial function determined?

The degree of a polynomial function is determined by the highest power of the variable term, unless the coefficient of that term is zero.

Q: Are all functions with variables raised to non-negative powers considered polynomial functions?

No, for a function to be a polynomial function, the variable terms must have non-negative integral powers. Fractional or negative powers make a function non-polynomial.

Summary & Key Takeaways

• Polynomial functions are functions that involve one variable raised to unique powers.

• The terms of a polynomial function have non-negative integral powers and real coefficients.

• The degree of a polynomial function is determined by the highest power of the variable term, unless the coefficient of that term is zero.