What is the quotient and remainder if any when the polynomial 2x quadrupled -9x cubed plus 13x squared -15x plus 9 is divided by x -3?

Answer 1

2x4 - 9x3 + 13x2 - 15x + 9

= 2x4 - 6x3 - 3x3 + 9x2 + 4x2 - 12x - 3x + 9

= 2x3(x - 3) - 3x2(x - 3) + 4x(x - 3) - 3(x - 3)

= (x - 3)*(2x3 - 3x2 + 4x - 3)

So the quotient is (2x3 - 3x2 + 4x - 3)

and the remainder is 0.