Classify the following as linear, quadratic and cubic polynomials:

Solution:

We know that,

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.

(i) x2+x

Solution:

The highest power of x2+x is 2

the degree is 2

Hence, x2+x is a quadratic polynomial

(ii) x–x3

Solution:

The highest power of x–x3 is 3

the degree is 3

Hence, x–x3 is a cubic polynomial

(iii) y+y2+4

Solution:

The highest power of y+y2+4 is 2

the degree is 2

Hence, y+y2+4is a quadratic polynomial

(iv) 1+x

Solution:

The highest power of 1+x is 1

the degree is 1

Hence, 1+x is a linear polynomial.

(v) 3t

Solution:

The highest power of 3t is 1

the degree is 1

Hence, 3t is a linear polynomial.

(vi) r2

Solution:

The highest power of r2 is 2

the degree is 2

Hence, r2is a quadratic polynomial.

(vii) 7x3

Solution:

The highest power of 7x3 is 3

the degree is 3

Hence, 7x3 is a cubic polynomial.