Verify division a

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