62 how many degrees are in the polynomial? And name the polynomial using the number of terms and the degree

Answer 1

Hi Alex,

here is some basic vocabulary.

A polynomial is an expression that has many unlike terms, separated by a plus or minus symbol.

A polynomial with 2 terms and a polynomial with 3 terms have special names.

Example 1: a+2 is a binomial ,or it is a polynomial with 2 unlike terms separated by a plus symbol.

Example 2: 2x+3y-5

is a trinomial; or it is a polynomial with 3 unlike terms.

What are the 3 terms ? The 3 terms are 2x, 3y, and 5.

What is the degree of this polynomial ?

The degree of this trinomial is 1.

Why?

The degree is 1 because 1 is the highest power (or exponent) of a variable in the polynomial. [Invisible exponent means that the exponent is 1]

Example 3; 5x²-2y+6 is a trinomial and the degree is 2.

Example 4: x+ y is a binomial. Do you know why? ( Hint: what does the bi in bicycle tell you?)

What is the degree of this binomial?

All expressions with 4 or more terms are Polynomials!

Example 5: a³+ 7a+ 2b + 5b² + 8 is a polynomial . It has 5 terms and the degree of this polynomial is 3.

Note.

The following expressions are called terms or monomials.

(i) x (ii) x² (iii) xy (iv) 3xz (v) -7abc (vi) 4

In the term 3xz, the 3 is called the coefficient ; 3 is called the number part and xz is called the variable part.

The term 4 is a constant .