Originally Posted by **ticbol**

I have not studied before how to do synthetic division using (ax +b). It was by (x +a) only. So I'd reduce the (ax +b) into (x +c), then do it as usual.

In doing that, I'd divide all by the coefficient of the x in the (ax +b).

(4x^3 -8x^2 -11x +9) / (2x +3)

I'd divide everything by 2,

(2x^3 -4x^2 -5.5x +4.5) / (x +1.5)

and do the usual synthetic division.

..-1.5..|....2....-4....-5.5....4.5

.....................-3....10.5...-7.5

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...............2....-7.....5.......-3 <----there is a remainder of (-3). That means (2x +3) is not a factor of 4x^3 -8x^2 -11x +9.