Question

Rewrite the expression x^3+10x^2+13x+39/x^2+2x+1 in the form q(x)+r(x)/b(x).

Answer 1

by long dividing:
=(x+8) + (31-4x)/(x^2+2x+1)

Answer 2

`(x+8) + (-4x+31)/(x^2+2x+1)`

Explanation:

x^3+10x^2+13x+39/x^2+2x+1

`(x^3+10x^2+13x+39)/(x^2+2x+1)`

We divide it using long division

x +8

-----------------------------------------

`x^2+2x+1`
`x^3+10x^2+13x+39`

`x^3+2x^2+x`

------------------------------------------(subtract)

`8x^2+12x+39`

`8x^2+16x+8`

-------------------------------------------

`-4x+31`

Quotient is x+8

Remainder is -4x+3

We write it in the form q(x)+r(x)/ b(x)

`(x+8) + (-4x+31)/(x^2+2x+1)`