Question

I have no idea how this is worked out but the question is find the quotient and remainder of x^3-x^2-3 / x+1

Answer 1

Synthetic division

We want to solve the following division:

`(x^3-x^2-3​)/(x+1)`

Using the following division we want to locate the polynomials as shown in the next figure:

We have that the polynomial of the red square is:

`x^3-x^2-3`

we have that its coefficients (the number behind each terms) are:

for x³: 1

for x²: -1

for x: 0

for numbers: -3

Then:

for the polynomial of the purple square (x - z) = (x + 1), we have that

x + 1 = x - (-1), then

x - (-1) = x - z

Then z = -1:

The numbers of the answer section are going to be the addition of each column, and they will be multiplied by z = -1, as the following figure shows:

In the answer section we will have the coefficients of the quotient, and the last number is the remainder:

Now, we have the answer

Answer - the quotient is:

x² -2x + 2

and the remainder is: -5