Polynomials

Exercise 2.1 Part 2

Question 3: Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Answer: `x^35 = 2 and x^100`

Question 4: Write the degree of each of the following polynomials:

(i) `5x^3 + 4x^2 + 7x`

Answer: Since, highest exponent of variable x = 3, thus degree of given polynomial = 3


(ii) `4 - y^2`

Answer: Since, highest exponent of variable y = 2, thus degree of given polynomial = 2

(iii) `5t - sqrt7`

Answer: Since, highest exponent of variable y = 1, thus degree of given polynomial = 1

(iv) 3

Answer: Since, polynomial having only a constant term is of zero degree.
Since, it has no variable and a constant polynomial is called as zero polynomial.


Question 5: Classify the following as linear, quadratic and cubic polynomials:

(i) `x^2 + x`

Answer: Quadratic
[A 2 degree polynomial is also called quadratic polynomial]

(ii) `x - x^3`

Answer: Cubic
[A 3 degree polynomial is also called cubic polynomial]

(iii) `y + y^2 + 4`

Answer: Quadratic
[A 2 degree polynomial is also called quadratic polynomial]

(iv) `1 + x`

Answer: Linear
[A one degree polynomial is called linear polynomial]

(v) `3t`

Answer: Linear
[A one degree polynomial is called linear polynomial]

(vi) `r^2`

Answer: Quadratic
[A two degree polynomial is called quadratic polynomial]

(vii) `7x^3`

Answer: Cubic
[A three degree polynomial is called cubic polynomial]



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