Question

Does (2x^3+ 15x^2 +27x + 5)/2x+5= (x^2+5x+1). Justify your answer.

Answer 1

Answer and explanation

We have given expression $\frac{2x^3+15x^2+27x+5}{2x+5}=x^2+5x+1$

We have to prove this

$\frac{2x^3+15x^2+27x+5}{2x+5}=x^2+5x+1$  can be written as ${2x^3+15x^2+27x+5}={2x+5}\times (x^2+5x+1)$

Now we have to prove L.H.S = R.H.S

Lets take R.H.S

So ${2x+5}\times (x^2+5x+1)=2x^3+10x^2+2x+5x^2+25x+5=2x^3+15x^2+27x+5$ = L.H.S

Hence proved