Yes; you are correct.
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The correct answer is:
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Answer choice: [C]: " x³ − 9x² + 23x − 12 " .
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Note: (a − b) (c − d + e) = ac − ad + ae − bc + bd − be ;
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(x − 4) (x² − 5x + 3) =
x * x² = x³ −
x * 5x = 5x² +
x * 3 = 3x −
4 * x² = 4x² −
-4 * 5x = -20x +
-4 * 3 = -12;
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(x − 4) (x² − 5x + 3) =
x³ − 5x² + 3x −4x² − (-20x) + (-12) ;
= x³ − 5x² + 3x −4x² + 20x − 12 ;
= x³ − 5x² − 4x² + 3x + 20x − 12 ;
= x³ − 9x² + 23x − 12 ; which is:
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Answer choice: [C]: " x³ − 9x² + 23x − 12 " .
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