If \(p(x)=x^3-3x^2-4x+12\), which of the following is a factor of \(p(x)\)?
Answer and explanation
Correct answer: \(x-2\)
By the factor theorem, if \(p(a)=0\), then \(x-a\) is a factor of \(p(x)\). Here, \(p(2)=2^3-3(2)^2-4(2)+12=8-12-8+12=0\), so \(x-2\) is a factor. In fact, \(p(x)=(x-2)(x-3)(x+2)\); the other given options are not factors. Exam tip: to test a possible linear factor \(x-a\), calculate \(p(a)\) directly.
Frequently asked questions
What is the correct answer to this question?
\(x-2\)
Why is this the correct answer?
By the factor theorem, if \(p(a)=0\), then \(x-a\) is a factor of \(p(x)\). Here, \(p(2)=2^3-3(2)^2-4(2)+12=8-12-8+12=0\), so \(x-2\) is a factor. In fact, \(p(x)=(x-2)(x-3)(x+2)\); the other given options are not factors. Exam tip: to test a possible linear factor \(x-a\), calculate \(p(a)\) directly.
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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