Answer:
Answer in the form [tex]\dfrac{r}{x+5}[/tex] is [tex]\dfrac{10}{x+5}.[/tex]
Step-by-step explanation:
1 step: Multiply [tex]x+5[/tex] by [tex]x^2[/tex] to get
[tex](x+5)x^2=x^3+5x^2[/tex]
and subtract the result from the polynomial [tex]x^3+6x^2+8x+25:[/tex]
[tex]x^3+6x^2+8x+25-(x^3+5x^2)=x^3+6x^2+8x+25-x^3-5x^2=x^2+8x+25.[/tex]
2 step: Multiply [tex]x+5[/tex] by [tex]x[/tex] to get
[tex](x+5)x=x^2+5x[/tex]
and subtract the result from the polynomial [tex]x^2+8x+25:[/tex]
[tex]x^2+8x+25-(x^2+5x)=x^2+8x+25-x^2-5x=3x+25.[/tex]
3 step: Multiply [tex]x+5[/tex] by [tex]3[/tex] to get
[tex](x+5)3=3x+15[/tex]
and subtract the result from the polynomial [tex]3x+25:[/tex]
[tex]3x+25-(3x+15)=3x+25-3x-15=10.[/tex]
Thus, the remainder is [tex]r=10.[/tex]
