SOLUTION: Could you please help me figure out binomials and polynomials such as 14x^3+4 and 3x^2y-21xy+3xy^2

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Question 118472This question is from textbook
: Could you please help me figure out binomials and polynomials such as 14x^3+4 and 3x^2y-21xy+3xy^2 This question is from textbook

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The "poly" in "polynomial" means "many".
technically, the term "polynomial" should only refer to sums of many terms, but the term is used to refer to anything from one_+term to a infinity many terms

the shorter polynomials do have their own names:

a first-degree polynomial such as 7x is sometimes called “linear” (or monic)

a one-term polynomial, such as 2x or 3x%5E3, may also be called a "monomial" ….mono=one

a two-term polynomial, such as 2x+%2B+%281%2F2%29+y, may also be called a "quadratic" or a "binomial" ….….bi=two

a three-term polynomial, such as +x+%2B+3y+%2B+2z or x4+%2B+3x2+%96+1, may also be called a "cubic" or a "trinomial"

a fourth-degree polynomial, such as x%5E4 or x%5E4+%96+6x%5E3+%2B+9, is sometimes called a "quartic" or a "bi-quadratic" polynomial

a fifth-degree polynomial, such as 2x%5E5 is sometimes called a "quintic"...and so on

so, answer to your question is:

14x%5E3%2B4+ is a two-term polynomial or a "binomial"

and 3x%5E2y-21xy%2B3xy%5E2 is a three-term polynomial or a "trinomial"