OpenStudy (anonymous):

Divide the following polynomials using synthetic division (x^3 - 2x^2 - 1) ( x - 1)

OpenStudy (mathmale):

First of all, have you done synth. div. before?

OpenStudy (mathmale):

If your divisor in long division is x-1, then the corresponding divisor for synth. div. is +1 (yes, that's the opposite sign).

OpenStudy (anonymous):

yes. my answer is x^2 - 2x + 1 1/x-1. but I received partial credit

OpenStudy (mathmale):

The given polynomial (which we call the dividend) is of the third order (the highest x power is 3). What are the coefficients of this polynomial? Think very carefully.

OpenStudy (mathmale):

Hint: x^3, x^2 and a constant show up in the given polynomial. What happened to the x?

OpenStudy (anonymous):

it was subtracted

OpenStudy (mathmale):

Actually, x does not show up at all where the 3rd term normally would be. So, in setting up your synth. div., you should use the coeff. 1 -2 0 and -1.

OpenStudy (mathmale):

Try doing this synth. div.: 1 | 1 -2 0 -1 ----------------- and see what you get.

OpenStudy (mathmale):

1 | 1 -2 0 -1 ----------------- 1

OpenStudy (anonymous):

1 -3 -3 2

OpenStudy (mathmale):

1 | 1 -2 0 -1 1 ----------------- 1 -1 Compare yours and mine. Can you finish the synth. div. now? If not, what do you need to know to do so?

OpenStudy (anonymous):

1 -1 -1 -2

OpenStudy (anonymous):

?

OpenStudy (mathmale):

that's great. 1, -1 and -1 are the coefficients of the quotient, which is what you wanted to find. That -2 is your remainder. Take these 3 coefficients, please, and write out the corresponding polynomial.

OpenStudy (anonymous):

x^2 - 1x - 1 2/x-1?