Advanced MathMediumConstant after dividing a difference of fourth powers
Advanced Math practice question
For all real x, the expression (x⁴ − 81)/(x² + 9) is equal to x² − c, where c is a constant. What is the value of c?
Answer: 9
x⁴ − 81 = (x² − 9)(x² + 9), so dividing by x² + 9 leaves x² − 9. Thus c = 9.
Common wrong answers
- If you answered 3
- 3 is √9, going one factoring step too far.
- If you answered 81
- 81 is the constant in the numerator, not c.
- If you answered -9
- −9 has the wrong sign.
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