find the quadratic and remainder when p(X) is divided by g(X) p(X)=30x^2-82x^2+11x^3+47-12x ,g(X)=3x^2+2x-4
Answers
Given f(x) = 30x^4 + 11x^3 - 82x^2 - 12x + 48.
Given g(x) = 3x^2 + 2x - 4.
Now,
We need to divide f(x) by g(x)
10x^2 - 3x - 12
-----------------------------------------------------
3x^2 + 2x - 4) 30x^4 + 11x^3 - 82x^2 - 12x + 48
30x^4 + 20x^3 - 40x^2
-------------------------------------------------------
- 9x^3 - 42x^2 - 12x + 48
-9x^3 - 6x^2 + 12x
--------------------------------------------------------
-36x^2 - 24x + 48
- 36x^2 - 24x + 48
------------------------------------------------------------
0
Verification:
= > Dividend = Divisor * Quotient + Remainder
= (3x^2 + 2x - 4) * (10x^2 - 3x - 12) + 0
= 30x^4 - 9x^3 - 36x^2 + 20x^3 - 6x^2 - 24x - 40x^2 - 12x + 48
= 30x^4 + 11x^3 - 82x^2 - 12x + 48