Advanced MathHardFactoring a quartic as a product of two quadratics
Advanced Math practice question
The expression x⁴ − 5x² + 4 is equal to (x² − a)(x² − b) for all x, where a and b are constants with a > b. What is the value of a − b?
Answer: 3
Treat x² as the variable: u² − 5u + 4 = (u − 4)(u − 1). So a = 4, b = 1, and a − b = 3.
Common wrong answers
- If you answered 4
- 4 is a alone, or the product ab.
- If you answered 5
- 5 is a + b, the sum of the constants.
- If you answered -3
- −3 has the wrong sign, since a > b.
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