Question

Classify the following as a constant, linear, quadratic and cubic polynomials:

(i) 2 – x² + x³

(ii) 3x³

(iii) 5t – √7

(iv) 4 – 5y²

(v) 3

(vi) 2 + x

(vii) y³ – y

(viii) 1 + x + x²

(ix) t² 

(x) √2x – 1

Answer 1

Constant polynomials: The polynomial of the degree zero.

Linear polynomials: The polynomial of degree one.

Quadratic polynomials: The polynomial of degree two.

Cubic polynomials: The polynomial of degree three.

(i) 2 – x² + x³

Powers of x = 2, and 3 respectively.

Highest power of the variable x in the given expression = 3

Hence, degree of the polynomial = 3

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

(ii) 3x³

Power of x = 3.

Highest power of the variable x in the given expression = 3

Hence, degree of the polynomial = 3

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

(iii) 5t – √7

Power of t = 1.

Highest power of the variable t in the given expression = 1

Hence, degree of the polynomial = 1

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

(iv) 4 – 5y²

Power of y = 2.

Highest power of the variable y in the given expression = 2

Hence, degree of the polynomial = 2

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

(v) 3

There is no variable in the given expression.

Let us assume that x is the variable in the given expression.

3 can be written as 3x⁰.

i.e., 3 = x⁰

Power of x = 0.

Highest power of the variable x in the given expression = 0

Hence, degree of the polynomial = 0

Since it is a polynomial of the degree 0, it is a constant polynomial.

(vi) 2 + x

Power of x = 1.

Highest power of the variable x in the given expression = 1

Hence, degree of the polynomial = 1

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

(vii) y³ – y

Powers of y = 3 and 1, respectively.

Highest power of the variable x in the given expression = 3

Hence, degree of the polynomial = 3

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

(viii) 1 + x + x²

Powers of x = 1 and 2, respectively.

Highest power of the variable x in the given expression = 2

Hence, degree of the polynomial = 2

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

(ix) t²

Power of t = 2.

Highest power of the variable t in the given expression = 2

Hence, degree of the polynomial = 2

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

(x) √2x – 1

Power of x = 1.

Highest power of the variable x in the given expression = 1

Hence, degree of the polynomial = 1

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