If (p(x)=4x+1) and (q(x)=4x-7), what type of polynomial is (p(x)-q(x))?
Answer and explanation
Correct answer: Constant polynomial
On subtracting, \(p(x)-q(x)=(4x+1)-(4x-7)=4x+1-4x+7=8\). The \(x\)-terms cancel, leaving the non-zero constant 8, so the result is a constant polynomial. A linear polynomial must have a non-zero coefficient of \(x\), which is absent here. Exam tip: While subtracting polynomials, change the sign of every term in the second bracket.
Frequently asked questions
What is the correct answer to this question?
Constant polynomial
Why is this the correct answer?
On subtracting, \(p(x)-q(x)=(4x+1)-(4x-7)=4x+1-4x+7=8\). The \(x\)-terms cancel, leaving the non-zero constant 8, so the result is a constant polynomial. A linear polynomial must have a non-zero coefficient of \(x\), which is absent here. Exam tip: While subtracting polynomials, change the sign of every term in the second bracket.
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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