If \(p(x)=x^3-3x^2-4x+12\), what is its complete factorised form?
Answer and explanation
Correct answer: \((x-3)(x-2)(x+2)\)
Grouping the terms gives \(p(x)=x^2(x-3)-4(x-3)\). Therefore, \(p(x)=(x-3)(x^2-4)=(x-3)(x-2)(x+2)\), so option A is correct. In option B, the first factor is incorrectly written as \(x+3\), whereas grouping clearly gives \(x-3\). In an exam, first extract the common binomial and then apply \(a^2-b^2=(a-b)(a+b)\).
Frequently asked questions
What is the correct answer to this question?
\((x-3)(x-2)(x+2)\)
Why is this the correct answer?
Grouping the terms gives \(p(x)=x^2(x-3)-4(x-3)\). Therefore, \(p(x)=(x-3)(x^2-4)=(x-3)(x-2)(x+2)\), so option A is correct. In option B, the first factor is incorrectly written as \(x+3\), whereas grouping clearly gives \(x-3\). In an exam, first extract the common binomial and then apply \(a^2-b^2=(a-b)(a+b)\).
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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