Question

divide x4-5x+6 by 2+x2 and verify division algorithm​

Answer 1

$f(x) = {x}^{4} - 5x + 6 \\ g(x) = {x}^{2} + 2$

x² - 2

x² + 2 | x^4 + 0x^3 + 0x² - 5x + 6

x^4 + 0 + 2x² + 0x + 0

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

- 2x² - 5x + 6

- 2x² + 0x - 4

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

- 5x + 10

q(x) = x² - 2

r(x) = -5x + 10

Division algorithm :

f(x) = g(x) * q(x) + r(x)

= [(x² + 2)*(x² - 2)] + (-5x + 10)

= x^4 + 2x² - 2x² - 4 - 5x + 10

= x^4 - 5x + 6

Hence, verified.

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