Which statement about p(x) = x^2 + 1 is correct?
Answer and explanation
Correct answer: It is a quadratic polynomial
The governing concept is classification by degree. The degree of a non-zero polynomial is the greatest exponent of the variable with a non-zero coefficient. In p(x) = x^2 + 1, the term x^2 has exponent 2 and coefficient 1, while 1 is the constant term. Thus the highest relevant exponent is 2, so the polynomial has degree 2 and is called quadratic. Therefore option B is correct. It is not linear because a linear polynomial has degree 1. It is certainly a polynomial because its variable has a non-negative integer exponent and the expression has finitely many terms. Option D incorrectly gives the degree as 1.
Frequently asked questions
What is the correct answer to this question?
It is a quadratic polynomial
Why is this the correct answer?
The governing concept is classification by degree. The degree of a non-zero polynomial is the greatest exponent of the variable with a non-zero coefficient. In p(x) = x^2 + 1, the term x^2 has exponent 2 and coefficient 1, while 1 is the constant term. Thus the highest relevant exponent is 2, so the polynomial has degree 2 and is called quadratic. Therefore option B is correct. It is not linear because a linear polynomial has degree 1. It is certainly a polynomial because its variable has a non-negative integer exponent and the expression has finitely many terms. Option D incorrectly gives the degree as 1.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Polynomials in one variable.
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