Question

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​

Answer 1

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

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3x^2 + 2x - 4) 30x^4 + 11x^3 - 82x^2 - 12x + 48

30x^4 + 20x^3 - 40x^2

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- 9x^3 - 42x^2 - 12x + 48

-9x^3 - 6x^2 + 12x

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-36x^2 - 24x + 48

- 36x^2 - 24x + 48

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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