What type of polynomial is x² + 5x + 6?
Answer and explanation
Correct answer: Quadratic
To classify a polynomial, identify the greatest power of the variable with a non-zero coefficient. In x² + 5x + 6, the term x² has exponent 2 and coefficient 1, which is non-zero. The remaining terms have degrees 1 and 0. Hence the polynomial has degree 2 and is called a quadratic polynomial. It is not linear because a linear polynomial has highest exponent 1. It is not cubic because there is no x³ term. It is also not the zero polynomial: the expression has several non-zero coefficients and is not identically equal to zero. Although it can be factored as (x + 2)(x + 3), factorisation does not change its degree or its classification.
Frequently asked questions
What is the correct answer to this question?
Quadratic
Why is this the correct answer?
To classify a polynomial, identify the greatest power of the variable with a non-zero coefficient. In x² + 5x + 6, the term x² has exponent 2 and coefficient 1, which is non-zero. The remaining terms have degrees 1 and 0. Hence the polynomial has degree 2 and is called a quadratic polynomial. It is not linear because a linear polynomial has highest exponent 1. It is not cubic because there is no x³ term. It is also not the zero polynomial: the expression has several non-zero coefficients and is not identically equal to zero. Although it can be factored as (x + 2)(x + 3), factorisation does not change its degree or its classification.
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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