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This is the second of our many quizzes on classifying polynomials. Click on this to access more such competitive quizzes on polynomials.

Classifying Polynomials Quiz 2

mathematics

 What is the degree of the zero polynomial?

 The constant polynomial ‘0’ is called the zero polynomial.  

 As we know that the zero polynomial is nothing but the constant polynomial ‘0’ or $f(t) = 0$. The degree of the zero polynomial or $f(t) = 0$ is not defined, because $f(t) = 0$, $p(t)=0t$ , $q(t)=0{{t}^{2}}$ , $r(t)=0{{t}^{3}}$ , $s(t)=0{{t}^{100}}$ etc. are equal to zero polynomial.  

 A polynomial of degree 1 is called the linear polynomial, a polynomial of degree 2 is called the quadratic polynomial, a polynomial of degree 3 is called a cubic polynomial etc. A polynomial with only a term is called a monomial, a polynomial with two terms is called a binomial, a polynomial with three terms is called a trinomial etc. 

 On comparing with all options (b) is correct as a linear polynomial may be a monomial or a binomial.<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/9d6f4af1-a0bc-4993-9cc4-10ac16b62ac61423543108845562408.png"/>

 Which of the following options is correct?

 Simplify each equation and check if the variable of a polynomial has the highest degree as 4.

 $\text{On comparing with the above options we have,} \\ p(x)=(7x+5)(3{{x}^{3}}-1) \\ \Rightarrow 21{{x}^{4}}-7x+15{{x}^{3}}-5 \\ \Rightarrow 21{{x}^{4}}+15{{x}^{3}}-7x-5 \\ \text{Clearly, there are 4 terms and the highest degree of variable “x” is 4.} \\ \text{So, this is a bi-quadratic quadrinomial} $

 Which of the following is not a cubic trinomial?  

 A polynomial of degree 3 is called a cubic polynomial and a polynomial with three terms is called a trinomial. 

 $\text{On comparing we have} \\ p(x)={{x}^{2}}(x+9x+1) \\ \Rightarrow {{x}^{2}}(10x+1) \\ \Rightarrow 10{{x}^{3}}+{{x}^{2}} \\ \text{Highest exponent of the variable “x” is 3 and total terms are 2.} \\ \text{It means the polynomial is a cubic binomial.} $

 Which of the following option is correct about the expression ${{x}^{3}}+7x{{y}^{2}}+\dfrac{3x}{yz}+z+31$? 

 In the polynomial, all the exponents in the algebraic expression must be non-negative integers.

 $\text{Let, } P(x)={{x}^{3}}+7x{{y}^{2}}+\dfrac{3x}{yz}+z+31 \\ \Rightarrow {{x}^{3}}+7x{{y}^{2}}+3x{{y}^{-1}}{{z}^{-1}}+z+31 \\ \text{As we know that a polynomial cannot contain negative exponents.} \\ \text{It means the given expression is not a polynomial. } $