Question

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

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

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.

Answer 5

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

Answer 6

it was subtracted

Answer 7

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.

Answer 8

Try doing this synth. div.:

1 | 1 -2 0 -1

-----------------

and see what you get.

Answer 9

1 | 1 -2 0 -1

-----------------
1

Answer 10

1 -3 -3 2

Answer 11

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?

Answer 12

1 -1 -1 -2

Answer 13

?

Answer 14

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.

Answer 15

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