Answer and explanation
We have given expression [tex]\frac{2x^3+15x^2+27x+5}{2x+5}=x^2+5x+1[/tex]
We have to prove this
[tex]\frac{2x^3+15x^2+27x+5}{2x+5}=x^2+5x+1[/tex] can be written as [tex]{2x^3+15x^2+27x+5}={2x+5}\times (x^2+5x+1)[/tex]
Now we have to prove L.H.S = R.H.S
Lets take R.H.S
So [tex]{2x+5}\times (x^2+5x+1)=2x^3+10x^2+2x+5x^2+25x+5=2x^3+15x^2+27x+5[/tex] = L.H.S
Hence proved
