## Problems on Algebra-I In this page 'Problems on algebra-I' we are going to see problems on coefficient of the terms, and degree of the polynomial.

Parents and teachers can guide the students to do the problems on their own. If they are having any doubt they can verify the solutions.

### Problems on algebra-I

1.  State which of the following expressions are polynomials in one variable or not. Give reasons for your answer.

(i)     2x  - x³ +x-6

(ii)    3x²- 2x+1

(iii)       y³ +2√3

(iv)       x - 1/x

(v)       ∛t+2t

(vi)       x³ + y³ +z

2.    Write the coefficient of x² and x in each of the following:

(i)       2+3x-4x²+x³

(ii)     √3x + 1

(iii)    x³ + √2x² + 4x-1

(iv)     1/3 x² +x+6

Degree of the polynomials

" Degree of the polynomial is the highest degree term with non zero coefficients in a polynomial. "

The following problems based on degree of the polynomials.

3.    Write the degree of each of the following polynomials.

(i)     4- 3x²

(ii)    5y+√2

(iii)  12-x+4x³

(iv)   5

Types of polynomials

Based on the degree:

• Constant polynomial: A polynomial of degree zero is called a constant polynomial.
• Linear polynomial: A polynomial of degree one is called a linear polynomial.
• Quadratic polynomial: A polynomial of degree two is called a quadratic polynomial.
• Cubic polynomial: A polynomial of degree three is called a cubic polynomial.

Based on the terms:

• Monomial : Polynomials which have only one term are known as monomials.
• Binomial: Polynomials which have only two terms are called binomials.
• Trinomial: Polynomials which have three terms are called trinomials.

The following problems based on the types of polynomials.

4.     Classify the following polynomials based on their degree.

(i)     3x² + 2x +1

(ii)     4x³ -1

(iii)    y+3

(iv)    y² - 4

(v)     4x³

'(vi)   2x

5.    Give one example of a binomial of degree 27 and monomial of degree 49 and trinomial of degree 36.

Students can try to solve the problems on their own. Parents and teachers can encourage the students to do so. If they are having any doubt they can verify the solutions.  If you are having any further doubt you can contact us through mail, we will help you to clear your doubt.