16Hit1600
Advanced MathHardCoefficient of x² in a product of three linear factors

Advanced Math practice question

When (x − 2)(x + 3)(x − 5) is expanded, what is the coefficient of x²?

Answer: -4

The x² coefficient of (x − a)(x − b)(x − c) is −(a + b + c). Here a + b + c = 2 + (−3) + 5 = 4, so the coefficient is −4. (Full expansion: x³ − 4x² − 11x + 30.)

Common wrong answers

If you answered 4
4 has the wrong sign.
If you answered 30
30 is the constant term.
If you answered -11
−11 is the coefficient of x.

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