Polynomial Vocabulary & Standard Form
A polynomial is a sum of terms like . Standard form lines those terms up from the highest power of down to the constant.
Putting a polynomial in standard form makes its degree and leading coefficient easy to read — and those two features drive everything from end behavior to the number of roots.
Standard form and degree
Standard form writes terms in order of decreasing exponent. The degree is the highest exponent; the leading coefficient is the number in front of that highest-degree term.
For , the degree is and the leading coefficient is . A constant term has degree zero.
Naming polynomials
Polynomials are named by degree — linear (1), quadratic (2), cubic (3), quartic (4) — and by number of terms — monomial, binomial, trinomial.
Rearranging a scrambled polynomial into standard form is usually the first step of any problem, so it becomes automatic.
Worked examples
Example 1: standard form
Write in standard form.
Answer:
Example 2: degree and leading coefficient
Give the degree and leading coefficient of .
Answer: Degree , leading coefficient
Example 3: naming by degree and number of terms
Name by its degree and by its number of terms.
Answer: A quadratic trinomial
Try one yourself
Common questions
What is standard form?
Terms written from highest degree to lowest. It makes the degree and leading coefficient easy to spot.
What is the degree of a polynomial?
The largest exponent on the variable. A constant has degree zero, and a linear term has degree one.
What is the leading coefficient?
The number multiplying the highest-degree term. In , it is .
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