Advanced MathVery hardFactoring a difference of cubes
Advanced Math practice question
The polynomial x³ − 8 can be written as (x − 2)(x² + bx + c), where b and c are constants. What is the value of b + c?
Answer: 6
Expanding (x − 2)(x² + bx + c) and matching: the x² terms give b − 2 = 0, so b = 2; the constant gives −2c = −8, so c = 4. Then b + c = 6.
Common wrong answers
- If you answered 2
- 2 is b alone.
- If you answered 4
- 4 is c alone.
- If you answered -2
- −2 takes b = −2 from the sign of (x − 2), but the x² terms must cancel.
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