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For the polynomial \(p(x)=2x^3-3x^2-11x+6\), a student finds that \(p(3)=0\) and concludes that \(x+3\) is a factor. What is the correct correction to the student's conclusion?
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Answer and explanation
Correct answer: If \(p(3)=0\), then \(x-3\) is a factor.
By the Factor Theorem, if \(p(a)=0\), then \(x-a\) is a factor. Here, \(2(3)^3-3(3)^2-11(3)+6=0\), so \(x-3\) is correct, not \(x+3\). In exams, remember to reverse the sign in the factor.
Frequently asked questions
What is the correct answer to this question?
If \(p(3)=0\), then \(x-3\) is a factor.
Why is this the correct answer?
By the Factor Theorem, if \(p(a)=0\), then \(x-a\) is a factor. Here, \(2(3)^3-3(3)^2-11(3)+6=0\), so \(x-3\) is correct, not \(x+3\). In exams, remember to reverse the sign in the factor.
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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