Question

x^4-5x^3+5x^2+5x-6;x-3.Divide the polynomial by the binomial.

Answer 1

Hi friend ✋✋✋✋
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Your answer
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To divide (x⁴ - 5x³ + 5x² - 6) by (x - 3) .

Factorising it by using factor theorem.
Now,
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x⁴ - 5x³ + 5x² + 5x - 6

=> x⁴ - 3x³ - 2x³ + 6x² - x² + 3x + 2x - 6

=> x³(x - 3) - 2x²(x - 3) - x(x - 3) + 2(x - 3)

=> (x - 3)(x³ - 2x² - x + 2)

Now,
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Dividing it by (x - 3) ,we get ,
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(x - 3)(x³ - 2x² - x + 2)/(x - 3)

=> (x³ - 2x² - x + 2)

HOPE IT HELPS