polynomial
posted by kingwendu .
given that the expression ax^311x^2+bx+2 is exactly divisible by 2x^23x2, find a and b then factorise completly (do not use long division).

(cxd)(2x^2  3x  2) = ax^3  11x^2 + bx + 2
2cx^3  (3c+2d)x^2  (2c3d)x + 2d = ax^3  11x^2 + bx + 2
2c = a
3c+2d = 11
2c3d = b
2d = 2
so,
d=1
3c+2=11
c=3
3 = b
a = 6
check:
(3x1)(2x^2  3x  2) =
6x^3  11x^2  3x + 2