What is the product of p(1) and p(−1) for p(x)=2x³+x²−5x+2?
Answer and explanation
Correct answer: 0
The governing concept is direct evaluation of a polynomial at specified values, followed by multiplication. For x = 1, p(1) = 2(1)³ + (1)² − 5(1) + 2 = 2 + 1 − 5 + 2 = 0. For x = −1, carefully preserve the odd-power sign: p(−1) = 2(−1)³ + (−1)² − 5(−1) + 2 = −2 + 1 + 5 + 2 = 6. Thus p(1)p(−1) = 0 × 6 = 0, making option C correct. Once one factor is zero, the product is zero regardless of the other factor. Options A, B, and D arise from substitution, sign, or multiplication errors. The corrected answer is C, not A.
Frequently asked questions
What is the correct answer to this question?
0
Why is this the correct answer?
The governing concept is direct evaluation of a polynomial at specified values, followed by multiplication. For x = 1, p(1) = 2(1)³ + (1)² − 5(1) + 2 = 2 + 1 − 5 + 2 = 0. For x = −1, carefully preserve the odd-power sign: p(−1) = 2(−1)³ + (−1)² − 5(−1) + 2 = −2 + 1 + 5 + 2 = 6. Thus p(1)p(−1) = 0 × 6 = 0, making option C correct. Once one factor is zero, the product is zero regardless of the other factor. Options A, B, and D arise from substitution, sign, or multiplication errors. The corrected answer is C, not A.
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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