In which option is the sum of two linear polynomials a constant polynomial?
Answer and explanation
Correct answer: \(3x+4\), \(-3x+5\)
In option B, \((3x+4)+(-3x+5)=3x-3x+4+5=9\). The \(x\)-terms cancel each other, so the sum is the constant polynomial \(9\). In option C, the constant terms cancel, but the sum is \(2x\), which is a linear polynomial. Exam tip: for the sum to be a constant, the coefficients of \(x\) in the two polynomials must be opposites.
Frequently asked questions
What is the correct answer to this question?
\(3x+4\), \(-3x+5\)
Why is this the correct answer?
In option B, \((3x+4)+(-3x+5)=3x-3x+4+5=9\). The \(x\)-terms cancel each other, so the sum is the constant polynomial \(9\). In option C, the constant terms cancel, but the sum is \(2x\), which is a linear polynomial. Exam tip: for the sum to be a constant, the coefficients of \(x\) in the two polynomials must be opposites.
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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