Division Algorithm for Polynomials

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following

p(x) = x³ – 3x² + 5x – 3, g(x) = x² – 2

Obtain all other zeroes of 3x⁴ + 6x³ – 2x² – 10x – 5, if two of its zeroes are `sqrt(5/3)` and - `sqrt(5/3)`

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = x³ − 6x² + 11x − 6, g(x) = x² + x + 1

What must be subtracted from the polynomial f(x) = x⁴ + 2x³ − 13x² − 12x + 21 so that the resulting polynomial is exactly divisible by x² − 4x + 3 ?

On dividing x³ – 3x² + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x)

Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 4x³ + 8x² + 8x + 7, g(x) = 2x² − x + 1

Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial 

x² + 3x + 1, 3x⁴ + 5x³ – 7x² + 2x + 2

Find the quotient and remainder of the following.

(−18z + 14z² + 24z³ + 18) ÷ (3z + 4)