If \(p(x)=x^3-3x^2+3x-1\), what is the value of \(p(2)\)?
Answer and explanation
Correct answer: 1
The polynomial can be written as \(p(x)=x^3-3x^2+3x-1=(x-1)^3\). Hence, \(p(2)=(2-1)^3=1\), so option B is correct. Option C incorrectly treats the input value 2 as the value of the polynomial. Exam tip: Look for the identity \(a^3-3a^2b+3ab^2-b^3=(a-b)^3\) before expanding and calculating term by term.
Frequently asked questions
What is the correct answer to this question?
1
Why is this the correct answer?
The polynomial can be written as \(p(x)=x^3-3x^2+3x-1=(x-1)^3\). Hence, \(p(2)=(2-1)^3=1\), so option B is correct. Option C incorrectly treats the input value 2 as the value of the polynomial. Exam tip: Look for the identity \(a^3-3a^2b+3ab^2-b^3=(a-b)^3\) before expanding and calculating term by term.
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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