Question

Polynomial division box method

Fill in the missing values below one at a time to find the quotient when 4x^3 + x + 5 is divided by x + 1

Answer 1

To find the quotient when 4x^3 + x + 5 is divided by x + 1, we can use long division. First, we divide 4x^3 by x to get 4x^2. Then we multiply x + 1 by 4x^2 to get 4x^3 + 4x^2. We subtract this from 4x^3 + x + 5 to get -4x^2 + x + 5.

We bring down the next term, which is 0x^2, and repeat the process. We divide -4x^2 by x to get -4x. Then we multiply x + 1 by -4x to get -4x^2 - 4x. We subtract this from -4x^2 + x + 5 to get 5x + 5.

We divide 5x by x to get 5, and multiply x + 1 by 5 to get 5x + 5. We subtract this from 5x + 5 to get a remainder of 0.

Therefore, the quotient is 4x^2 - 4x + 5.