## Solutions to algebra-I

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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) 2x⁵ - 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 +z⁶

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 = cy⁴⁹
- Trinomial of degree 36 = ax³⁶ + bx⁶ + 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.

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