Alg 2 question find the quotient and remainder for (2x^3 + 9x^2 + 11x + 3) ÷ (2x + 3).

quotient: x² +3x +1

remainder: 0

Step-by-step explanation:

You can use polynomial long division or synthetic division for the purpose. I have chosen synthetic division be cause it is faster and more compact.

Synthetic division works best if the binomial divisor has a leading coefficient of 1. For that to be the case, we need to divide the divisor by 2 to make it be (x + 3/2). Then the zero we use for the synthetic division is -3/2, and the quotient will be a factor of 2 larger than it would be had we used the original divisor.

Our result from synthetic division is a quotient of 2x^2 +6x +2 and a remainder of 0. Dividing this quotient by 2 gives the quotient for your problem: x^2 +3x +1.