If \(p(x)=x^3-1\), which of the following is a linear factor of the polynomial?
Answer and explanation
Correct answer: \(x-1\)
Using the difference-of-cubes identity, \(x^3-1^3=(x-1)(x^2+x+1)\). Hence, \(x-1\) is a linear factor of the polynomial. The other options are not factors because \(p(-1)=-2\), \(p(3)=26\), and \(p(-3)=-28\); thus, \(-1,3,-3\) are not zeroes. Exam tip: apply \(a^3-b^3=(a-b)(a^2+ab+b^2)\) when factoring a difference of cubes.
Frequently asked questions
What is the correct answer to this question?
\(x-1\)
Why is this the correct answer?
Using the difference-of-cubes identity, \(x^3-1^3=(x-1)(x^2+x+1)\). Hence, \(x-1\) is a linear factor of the polynomial. The other options are not factors because \(p(-1)=-2\), \(p(3)=26\), and \(p(-3)=-28\); thus, \(-1,3,-3\) are not zeroes. Exam tip: apply \(a^3-b^3=(a-b)(a^2+ab+b^2)\) when factoring a difference of cubes.
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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