Advanced MathMediumConstant in a product that telescopes to a difference of powers
Advanced Math practice question
The product (x − 1)(x + 1)(x² + 1) is equal to x⁴ − c for all x, where c is a constant. What is the value of c?
Answer: 1
(x − 1)(x + 1) = x² − 1, and (x² − 1)(x² + 1) = x⁴ − 1. So c = 1.
Common wrong answers
- If you answered 0
- 0 would mean the product is x⁴, but the constant terms multiply to −1.
- If you answered 2
- 2 comes from adding the constants 1 + 1 in the last two factors.
- If you answered -1
- −1 has the wrong sign; the product is x⁴ − 1, so c = +1.
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