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If p(x) = x^3 + 3x^2 - 4x - 12, which of the following is a factor of p(x)?
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Answer and explanation
Correct answer: x + 3
By the factor theorem, (x - a) is a factor of p(x) if p(a) = 0. Here, p(-3) = (-3)^3 + 3(-3)^2 - 4(-3) - 12 = -27 + 27 + 12 - 12 = 0. Therefore, (x + 3) is a factor. As an exam tip, for a possible factor x + a, substitute x = -a; the polynomial must evaluate to zero.
Frequently asked questions
What is the correct answer to this question?
x + 3
Why is this the correct answer?
By the factor theorem, (x - a) is a factor of p(x) if p(a) = 0. Here, p(-3) = (-3)^3 + 3(-3)^2 - 4(-3) - 12 = -27 + 27 + 12 - 12 = 0. Therefore, (x + 3) is a factor. As an exam tip, for a possible factor x + a, substitute x = -a; the polynomial must evaluate to zero.
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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