On dividing 3x3 + x2 + 2x + 5 by a polynomial g(X), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).

We know that,

According to the division rule, we have


Dividend = Quotient × Divisor + Remainder


Here, we have:


Dividend = 3x3 + x2 + 2x + 5


Quotient = 3x – 5


Remainder = 9x + 10


Putting these values in the formula, we get


3x3 + x2 + 2x + 5 = 3x – 5 × g (x) + 9x + 10


3x3 + x2 + 2x + 5 – 9x – 10 = (3x – 5) × g(x)


3x3 + x2 – 7x – 5 = (3x – 5) × g (x)


g (x) =



∴ g (x) = x2 + 2x + 1


10