If p(x) = x³ − 4x, what is the value of p(−2) + p(2)?
Answer and explanation
Correct answer: 0
p(−2) = (−2)³ − 4(−2) = −8 + 8 = 0, and p(2) = 2³ − 4(2) = 8 − 8 = 0. Therefore, p(−2) + p(2) = 0 + 0 = 0. Also, p(x) is an odd polynomial, so p(−x) = −p(x), making the sum for opposite inputs zero. Exam tip: Check whether the polynomial is odd before calculating both values.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
p(−2) = (−2)³ − 4(−2) = −8 + 8 = 0, and p(2) = 2³ − 4(2) = 8 − 8 = 0. Therefore, p(−2) + p(2) = 0 + 0 = 0. Also, p(x) is an odd polynomial, so p(−x) = −p(x), making the sum for opposite inputs zero. Exam tip: Check whether the polynomial is odd before calculating both values.
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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