## Solutions to algebra-I

In this page, 'Solutions to algebra-I' we are discussing how to do the problems given in problems on algebra-I.

### Solutions to 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

Solution:  Polynomial in one variable.

(ii)    3x²- 2x+1

Solution:  Polynomial in one variable.

(iii)       y³ +2√3

Solution:   Polynomial in one variable.

(iv)       x - 1/x

Solution:   Since the exponent of x is not a whole number, it is not a polynomial.

(v)       ∛t+2t

Solution:  Since the exponent of t is not a whole number, it is not a polynomial.

(vi)       x³ + y³ +z

Solution:  It is a polynomial in three variables.

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

(i)       2+3x-4x²+x³

Solution:   Coefficient of x² is -4

Coefficient of    x  is 3

(ii)     √3x + 1

Solution:   Since there is no x² term, the coefficient  is 0.

Coefficient of x is √3

(iii)    x³ + √2x² + 4x-1

Solution:      Coefficient of  x² is √2

Coefficient of x is      4

(iv)     1/3 x² +x+6

Solution:       Coefficient of  x² is 1/3

Coefficient of x is 1

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

(i)     4- 3x²

Solution:   Degree of the polynomial is 2.

(ii)    5y+√2

Solution:   Degree of the polynomial is 1.

(iii)  12-x+4x³

Solution:   Degree of the polynomial is 3.

(iv)   5

Solution:   Degree of the polynomial is 0.

4.     Classify the following polynomials based on their degree.

(i)     3x² + 2x +1

Solution:   Since the degree of the polynomial is 2, it is a quadratic equation(polynomial).

(ii)     4x³ -1

Solution:   Since the degree of the polynomial is 3, it is a cubic equation(polynomial).

(iii)    y+3

Solution:   Since the degree of the polynomial is 1, it is a linear polynomial.

(iv)    y² - 4

Solution:   Since the degree of the polynomial is 2, it is a quadratic polynomial.

(v)     4x³

Solution:   Since the degree of the polynomial is 3, it is a cubic polynomial.

'(vi)   2x

Solution:   Since the degree of the polynomial is 1, it is a linear polynomial.

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

Solution:

• Binomial of degree 27 = ax²⁷+b
• Monomial of degree  49  =   cy
• Trinomial of degree 36    =   ax³⁶  + bx+ cx

Students can solve the problems on their own, compare the answer with the solutions discussed above in'Solutions to algebra-I'. If you are having any doubt you can contact us through mail, we will help you to clear your doubts.