Question

Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
(i) x+x²+7y² (ii) 3x-2
(iii) 2x+x2
(iv) 3y (v) t²+1
(vi) 7t⁴+4t³+3t-2

Answer 1

concept :

• standard equation of linear : ax + b
• standard equation of quadratic : ax² + bx + c
• standard equation of cubic : ax³ + bx² + cx + d
• standard equation of biquadratic : ax⁴ + bx³ + cx² + dx + e

now let's come to the question,

(i) x + x² + 7y² ,

here we see degree of polynomial is 2. so, it is quadratic polynomial.

(ii) 3x - 2

from above concept, it is clear that it is linear polynomial.

(iii) 2x + x² , it is quadratic polynomial.

(iv) 3y , it is linear polynomial.

(v) t² + 1 , it is quadratic polynomial.

(vi) 7t⁴ + 4t³ + 3t - 2, it is biquadratic polynomial.

Answer 2

Concept :  

Linear polynomial : A polynomial of degree is called a linear polynomial. In general, f(x) = ax + b  

Quadratic polynomial : A polynomial of degree 2 is known as quadratic polynomial.In general, f(x) = ax² + bx + c  

Cubic polynomial : A polynomial of degree 3 is called a cubic polynomial.In general, f(x) = ax³ + bx² + cx  + d

Bi quadratic polynomial : A fourth degree polynomial is called a bi quadratic polynomial.In general, f(x) = ax⁴ + bx³ + cx²  + dx + e

Degree : The exponent of the highest degree term in a polynomial is known as its degree.

 

(i) Given : Mistake in the question : x + x² + 4  

Here, the highest degree of a polynomial is 2. so, it is a quadratic polynomial.

 

(ii) Given : 3x - 2

Here, the highest degree of a polynomial is 1. so, it is a linear polynomial.

 

(iii) Given : 2x + x²  

Here, the highest degree of a polynomial is 2. so, it is a quadratic polynomial.

 

(iv) Given : 3y

Here, the highest degree of a polynomial is 1. so, it is a linear polynomial.

 

(v) Given : t² + 1

Here, the highest degree of a polynomial is 2. so, it is a quadratic polynomial.

 

(vi) Given : 7t⁴ + 4t³ + 3t - 2

Here, the highest degree of a polynomial is 4. so, it is a biquadratic polynomial.

 

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