Divide the polynomial x⁴ - 11x² …
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Gaurav Seth 5 years, 2 months ago
Given f(x) = x^4 - 11x^2 + 34x - 12.
Given g(x) = x - 2.
Now, we need to divide f(x) by g(x).
x^3 + 2x^2 - 7x + 20
-----------------------------------
x - 2) x^4 - 11x^2 + 34x - 12
x^4 - 2x^3
---------------------------------------
2x^3 - 11x^2 + 34x - 12
2x^3 - 4x^2
-------------------------------------------
-7x^2 + 34x - 12
- 7x^2 + 14x - 12
-------------------------------------
20x - 12
20x -40
------------------------------------
28
We know that Dividend = Divisor * Quotient + Remainder
= > (x - 2) * (x^3 + 2x^2 - 7x + 20) + 28
= > x^4 + 2x^3 - 7x^2 + 20x - 2x^3 - 4x^2 + 14x - 40 + 28
= > x^4 - 11x^2 + 34x - 12
= > Dividend
1Thank You