Question

If x - 4 is a factor of x³ - 6x² + 4x + 16, then find the other factor.

Answer 1

p(x) = x³ - 6x² + 4x + 16

g(x) = x - 4

x - 4 ) x³ - 6x² + 4x + 16 ( x² - 2x - 4

x³ - 4x²

------------

-2x² + 4x

-2x² + 8x

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-4x + 16

-4x + 16

--------------

0

f(x) = x² - 2x - 4

x = 2 ± √4 + 16 / 2

=> 2 ± √20 / 2

=> (2 + √20)/ 2 and (2 - √20)/2

Zeroes are:

$(i) \: 4 \\ (ii) \: \: \frac{2 + \sqrt{20} }{2} \\ (iii) \: \: \frac{2 - \sqrt{20} }{2}$