Verify division algorithm for the polynomials f(x) = 8 + 20x + x^{2} ‒ 6x^{3} and g(x) = 2 + 5x ‒ 3x^{2}.

It is given in the question that,

f (x) = - 6x^{3} + x^{2} + 20x + 8

g (x) = - 3x^{2} + 5x + 2

∴ Quotient = 2x + 3

Remainder = x + 2

We know that, according to division rule:

Dividend = Quotient × Divisor + Remainder

Putting the values in the above formula, we get:

- 6x^{3} + x^{2} + 20x + 8 = (- 3x^{2} + 5x + 2) (2x + 3) + (x + 2)

-6x^{3} + x^{2} + 20x + 8 = - 6x^{3} + 10x^{2} + 4x – 9x^{2} + 15x + 6 + x + 2

-6x^{3} + x^{2} + 20x + 8 = -6x^{3} + x^{2} + 20x + 8

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