16Hit1600
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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