Advanced MathHardCoefficient from a difference of areas
Advanced Math practice question
A rectangular garden has length 2x + 5 metres and width x − 1 metres, where x > 1. A square patio of side x metres is built inside it. The remaining garden area, in square metres, can be written as ax² + bx + c. What is the value of b?
Answer: 3
Garden area: (2x + 5)(x − 1) = 2x² + 3x − 5. Subtract the patio's x²: x² + 3x − 5, so b = 3.
Common wrong answers
- If you answered 1
- 1 is a, the coefficient of x².
- If you answered 7
- 7 adds the 5 and 2 from the length instead of combining the cross terms 5x and −2x.
- If you answered -5
- −5 is c, the constant term.
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