ACT Math Practice Question #1289 (Hard (34)) | Test Citadel
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ACT Math Difficulty: Hard (34)

Digital ACT Math Practice Question #1289

Test your problem-solving accuracy on this official-caliber item. Select an answer choice to check your reasoning instantly.

If the polynomial $f(x) = x^3 - 3x^2 + 4x - 12$ has a real root at $x = 3$, what are the other two roots of $f(x)$?
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Factor by grouping: $x^2(x-3) + 4(x-3) = 0 \implies x^2 + 4 = 0 \implies x = \pm 2i$.

Masterclass Solution & Distractor Trap Analysis

Factor by grouping: $$f(x) = x^2(x - 3) + 4(x - 3) = (x^2 + 4)(x - 3).$$ Setting $(x^2 + 4)(x - 3) = 0$ gives $x - 3 = 0 \implies x = 3$, and $x^2 + 4 = 0 \implies x^2 = -4 \implies x = \pm \sqrt{-4} = \pm 2i$. The remaining roots are imagi...

Distractor Analysis: Trap choice eliminates careless test-takers who confuse roots with coordinates...

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