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Verify division algorithm for the polynomials f(x) = 8 + 20x + x2 ‒ 6x3 and g(x) = 2 + 5x ‒ 3x2.
It is given in the question that,
f (x) = - 6x3 + x2 + 20x + 8
g (x) = - 3x2 + 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:
- 6x3 + x2 + 20x + 8 = (- 3x2 + 5x + 2) (2x + 3) + (x + 2)
-6x3 + x2 + 20x + 8 = - 6x3 + 10x2 + 4x – 9x2 + 15x + 6 + x + 2
-6x3 + x2 + 20x + 8 = -6x3 + x2 + 20x + 8