Question

( 2x^4+2x^3+x^2-x-1 ) \ ( x^2-x-1 )

Answer 1

`\frac{2 {x}^(4) + 2 {x}^(3) + 2 {x}^(2) + 2 {x}^(2) - x - 1 }{ {x}^(2) - x - 1 } = 2 {x}^(2) + 4x + 8 + \frac{11x + 7}{ {x}^(2) - x - 1 }`

Explanation:

We want perform the following polynomial division.

`\frac{2 {x}^(4) + 2 {x}^(3) + 2 {x}^(2) + 2 {x}^(2) - x - 1 }{ {x}^(2) - x - 1 }`

We carry out the polynomial division in the attachment to obtain:

`\frac{2 {x}^(4) + 2 {x}^(3) + 2 {x}^(2) + 2 {x}^(2) - x - 1 }{ {x}^(2) - x - 1 } = 2 {x}^(2) + 4x + 8 + \frac{11x + 7}{ {x}^(2) - x - 1 }`

See attachment;