Question

Divide using the division algorithm. Write your answer in the form Q + R/D where the degree of R is less than the degree of D. (2x ^ 3 + x ^ 2 - 2x - 1)/(x - 1)

Answer 1

`2x^(2)+3x+1+(0)/(x-1)`

Explanation:

First, we have to write down the problem in a division format. To do so, we take the constant term of the divisor with the opposite sign and write it to the left. After this, we write the coefficients of the dividend to the right.

Now, we write down the leading coefficient as is:

After this, multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line). Add the obtained result to the next coefficient of the dividend, and write down the sum.

Now we repeat this step with the next coefficient:

And then we repeat this step once again:

After this, we would have completed the division. We've obtained the resulting coefficients 2,3,1, and 0.

This way, we can conclude that the quotient is:

`2x^2+3x+1`

And the remainder is

`(0)/(x-1)=0`

This way, we can rewrite the quotient as:

`2x^2+3x+1+(0)/(x-1)`