Divide x^4
- 5x^3
+ 6 by 2 - x
^2
, and verify the division algorithm.
Answers
Answer:
Quotient= (-x^2-2)(−x
2
−2) and Remainder= (-5x+8)(−5x+8)
Step-by-step explanation:
Given : p(x)=x^4-5x+6p(x)=x
4
−5x+6 and g(x) = 2-x^2g(x)=2−x
2
To divide the p(x) by g(x)
We know, Dividend = Divisor × quotient + remainder
p(x)= Dividend , g(x)=Divisor
\frac{x^4-5x+6}{2-x^2}
2−x
2
x
4
−5x+6
= quotient + remainder
Solve by long division we get,
{\frac{x^4-5x+6}{2-x^2}=(-x^2-2)+(-5x+8)
By dividing we get,
Quotient= (-x^2-2)(−x
2
−2) and Remainder= (-5x+8)(−5x+8)
Step-by-step explanation:
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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