how do you divide (3x^4+7x^3-7x+2)/(3x-2) using synthetic division?

Question

mathmale · Answer

Your divisor is 3x-2; for synth. div. you'd set that = to 0 and solve the resulting equation for x:  3x-2=0 => x = 2/3.

Take the coefficients of    3x^4+7x^3-7x+2.  Important:  please note that there is no x^2 here.  This means that the coeff. of the x^2 term is 0.  You end up with 5 coefficients:
3  7  0  -7  2.

Here's the setup for synth div:
                     _____________________   
           2/3   /  3    7     0     -7     2

                   -----------------------

Know what to do next?  Bring the 3 down, as shown below:

           2/3   /  3    7     0     -7     2

                    -----------------------
                        3

Multiply that 3 by the divisor (2/3).  What do you get?  Write that number under the 7.

And so on.

algtrigcalc · Answer

3x^3+9x^2+6x-3

algtrigcalc · Answer

@mathmale

mathmale · Answer

Your result is correct.  Happy for that.  But you should finish the entire division in synthetic division, not moving back to long division.

algtrigcalc · Answer

|dw:1479956691602:dw| can you check what i did wrong here?