Question

Identify the coefficient of y 2 in 4y3
- 6y2
+ 3y -8

Answer 1

Step-by-step explanation:

Before you understand this topic you should read -

What is Algebraic Expression ?

What are Terms ?

An algebraic Expression with one or more terms is called Polynomials .

Eg. 2a, 5x + y, 2x2 + 3x + y, all are polynomials

If the variable in the polynomial is x, we may denote the polynomial by p(x) or q(x) or r(x) etc

For example: Polynomial 5x3 + 3x2 + x can be written as:

p(x) = 5x3 + 3x2 + x

Polynomial a3 + 2a + 3 can be written as:

q(a) = a3 + 2a + 3

Polynomial r2 + r + 35 can be written as:

f(r) = r2 + r + 35

A polynomial can have any number of terms.

Polynomials can be of following types:

Zero Polynomial

Monomial

Binomial

Trinomial

(You can study these types from the above provided link)

Have a look at the below expression and study what are terms, constant term, variables, power and coefficients of Polynomial.

3x2 + 2x + 2

Terms in given Polynomial are : 3x2 + 2x + 2

Constant Term in given Polynomial is : 3x2 + 2x + 2

Variables in given Polynomial are : 3x2 + 2x + 2

Power / Exponent in given Polynomial is : 3x2 + 2x + 2

Coefficients in given Polynomial are : 3x2 + 2x + 2

Note: If Power or Exponent is negative then it is not a polynomial . For example x-2 or 2x-2

Let's study few examples and find terms, constant term, variables, power and coefficients of Polynomial

Example - 1 : Find terms, constant term, variables, power and coefficients from 4y2 + 5x + 3

Solution : The given Polynomial is 4y2 + 5x + 3 so

Terms in given Polynomial are : 4y2 + 5x + 3

Constant Term in given Polynomial is : 4y2 + 5x + 3

Variables in given Polynomial are :4y2 + 5x + 3

Power in given Polynomial is : 4y2 + 5x + 3

Coefficient in given Polynomial are : 4y2 + 5x + 3

Example - 2 : Find terms, constant term, variables, power and coefficients from 5y2 + 6x - 4

Solution : The given Polynomial is 5y2 + 6x - 4 so

Terms in given Polynomial are : 5y2 + 6x - 4

Constant Term in given Polynomial is : 5y2 + 6x - 4

Variables in given Polynomial are : 5y2 + 6x - 4

Power in given Polynomial is : 5y2 + 6x - 4

Coefficient in given Polynomial are : 5y2 + 6x - 4