Question

What is the quotient (3x3 − x2 − x − 1) ÷ (x − 1)?

Answer 1

Using the long division or synthetic division we can get 3x^2+2x+1

Answer 2

The quotient is
`3x^(2) + 2x + 1`

Explanation:

To find the quotient we use synthetic division

Step 1 : Arrange the given polynomial in descending order if not arranged.The given polynomial is
`3x^(3)-x^(2)-x-1`. List only the cofficients in division table.

Step 2 : Place 0 down the leading coefficients. and then add the two numbers and write the result.

Step 3 : Multiply the number in the division box with the number written down after addition and write result in next column.

Step 4 : Continue in the same way up to the last column.

Step 5 : Write the final answer such that the bottom row with the first element written with the coefficients of power less that 1 with the original polynomial. And also the last number will be remainder and written as fraction.

Hence, from the table of synthetic division which i attached the quotient will be

`3x^(2) + 2x + 1`