Divide x4
- 5x3
+ 6 by 2 - x
2
, and verify the division algorithm.
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Step-by-step explanation:
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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