If (p(x)=x+3r) and (q(x)=x-5r), what type of polynomial is (p(x)-q(x))?
Answer and explanation
Correct answer: Constant polynomial
\(p(x)-q(x)=(x+3r)-(x-5r)=x+3r-x+5r=8r\). The terms containing \(x\) cancel, so no power of \(x\) remains. Hence, treating \(r\) as a constant, \(8r\) is a constant polynomial in \(x\). A linear polynomial must contain an \(x\)-term, so option A is not correct. Exam tip: identify the variable with respect to which the polynomial is being classified.
Frequently asked questions
What is the correct answer to this question?
Constant polynomial
Why is this the correct answer?
\(p(x)-q(x)=(x+3r)-(x-5r)=x+3r-x+5r=8r\). The terms containing \(x\) cancel, so no power of \(x\) remains. Hence, treating \(r\) as a constant, \(8r\) is a constant polynomial in \(x\). A linear polynomial must contain an \(x\)-term, so option A is not correct. Exam tip: identify the variable with respect to which the polynomial is being classified.
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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