For the polynomial \(p(x)=x^3-8\), which calculation proves that \(p(2)=0\)?
Answer and explanation
Correct answer: \(p(2)=2^3-8=8-8=0\)
To find \(p(2)\), substitute 2 for \(x\): \(p(2)=2^3-8=8-8=0\). Hence, 2 is a zero of the polynomial. Option B incorrectly uses \(3^2\) instead of \(2^3\), while option C changes the exponent from 3 to 2. In an exam, remember that a number is a zero of a polynomial exactly when substitution gives a value of 0.
Frequently asked questions
What is the correct answer to this question?
\(p(2)=2^3-8=8-8=0\)
Why is this the correct answer?
To find \(p(2)\), substitute 2 for \(x\): \(p(2)=2^3-8=8-8=0\). Hence, 2 is a zero of the polynomial. Option B incorrectly uses \(3^2\) instead of \(2^3\), while option C changes the exponent from 3 to 2. In an exam, remember that a number is a zero of a polynomial exactly when substitution gives a value of 0.
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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