If \(p(x)=0\cdot x-6\), is it a linear polynomial?
Answer and explanation
Correct answer: No, it is a constant polynomial
Since \(0\cdot x=0\), we get \(p(x)=0-6=-6\). The coefficient of \(x\) is zero, so there is no non-zero variable term. Its degree is \(0\), making it a constant polynomial. A linear polynomial has the form \(ax+b\), where \(a\ne0\), so this is not linear. It is also not a zero polynomial because its value is \(-6\), not \(0\). Exam tip: simplify a polynomial before deciding its degree.
Frequently asked questions
What is the correct answer to this question?
No, it is a constant polynomial
Why is this the correct answer?
Since \(0\cdot x=0\), we get \(p(x)=0-6=-6\). The coefficient of \(x\) is zero, so there is no non-zero variable term. Its degree is \(0\), making it a constant polynomial. A linear polynomial has the form \(ax+b\), where \(a\ne0\), so this is not linear. It is also not a zero polynomial because its value is \(-6\), not \(0\). Exam tip: simplify a polynomial before deciding its degree.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear polynomials.
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