Answer:
see explanation
Explanation:
x - 2 | x² - x - 12
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x³ - 3x² - 10x + 24
x³ - 2x² ↓ ↓ ← subtract terms from terms above
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- x² - 10x + 24
- x² + 2x ↓ ← subtract terms from terms above
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- 12x + 24
- 12x + 24 ← subtract terms from above terms
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0 ← remainder
Since remainder is zero then (x - 2) is a factor
and quotient = x² - x - 12 , thus
x³ - 3x² - 10x + 24 = (x - 2)(x² - x - 12) = (x - 2)(x - 4)(x + 3)