Terms, Coefficients and Degrees

Algebraic term

Let us see few expressions

2x , 3p- q, 3x²b+ c³ -4ax .

2x has only one term. One term expressions are called monomials

3p-q has two terms 3p and -q

3p-q has two terms. 3p and -q, two term expressions are called binomials.

3x²b+ c³ – 4ax has three terms, 3x²b, c³ and -4ax. Three term expressions are called trinomials

To know how many terms, count number of ‘+’ or ‘–‘signs in the expression and add one 1 to it.

Number of terms = Number of ‘+’ or ‘ –’ signs + 1

Answers. 1) 2 terms

                2) 1 term

                3) 4 terms

                4) 1 term

Coefficients

We know how to find factors of numbers

Factors of 6 = 3 x 2, 6= 6 x 1.

Similarly, we can write factors of algebraic terms and expressions.

4xy = 4 * x* y. In algebra we do not use symbol ‘x’ for multiplication as it confuses with the alphabet x. Use dot or *

Degree of polynomial

In an expression or equation, highest power of the terms called degree of that expression or equation.

4x^5+x^3 y-3x-4

Power of first term is 5, second term is 3+1=4, power of 3^rd term is 1. Highest power is 5. So, Degree is 5

5x^6+4x^2-3  

  Degree 6

4a^4+8x^3-4x^2-9

 Degree 4

Try to name the expressions using degree and terms

4x^5+x^3 y-3x-4 

 Quintic polynomial with 4 terms

5x^6+4x^2-3

 Degree 6 trinomial

5x^4+4x^2

 Quartic binomial

Usually more than 3 terms expressions are called polynomials

Like and Unlike terms

Let us consider two terms 4x and -5x. In these, term 4x has two parts, numerical and variable part. If variable part of the terms is same or equal, they are called like terms. 4x and 3y are unlike terms. You can combine like terms. -4m + 3m = -1m=-m.