Question

Divide. If there is a remainder, express it in the form r/ x + 5 .

(x3+6x2+8x+25)÷(x+5)=

Answer 1

Answer in the form
`(r)/(x+5)` is
`(10)/(x+5).`

Explanation:

1 step: Multiply
`x+5` by
`x^2` to get

`(x+5)x^2=x^3+5x^2`

and subtract the result from the polynomial
`x^3+6x^2+8x+25:`

`x^3+6x^2+8x+25-(x^3+5x^2)=x^3+6x^2+8x+25-x^3-5x^2=x^2+8x+25.`

2 step: Multiply
`x+5` by
`x` to get

`(x+5)x=x^2+5x`

and subtract the result from the polynomial
`x^2+8x+25:`

`x^2+8x+25-(x^2+5x)=x^2+8x+25-x^2-5x=3x+25.`

3 step: Multiply
`x+5` by
`3` to get

`(x+5)3=3x+15`

and subtract the result from the polynomial
`3x+25:`

`3x+25-(3x+15)=3x+25-3x-15=10.`

Thus, the remainder is
`r=10.`