Question

Which of the following expressions is this one equivalent to?

Answer 1

We know that 
the euclid's division A/B implies A= BQ + R
wher Q = the quotient, and R is the remainder
after doing euclid's division, (3x^3+15x^2+17x+3)/x+5 = 3x²+17and R= - 82
so (3x^3+15x^2+17x+3= (3x²+17) (x+5) -82

the answer is x^3+15x^2+17x+3= (3x²+17) (x+5) - 82

Answer 2

Answer:

option (c) is correct,

$3x^2+17-\frac{82}{x+5}$ is the equivalent fraction to the given expression $\frac{3x^3+15x^2+17x+3}{x+5}$

Step-by-step explanation:

Given expression ,  $\frac{3x^3+15x^2+17x+3}{x+5}$

We have to choose an equivalent fraction from the given options.

Consider expression (c) ,

$3x^2+17-\frac{82}{x+5}$

Taking LCM , Multiply $3x^2+17$ by (x+5) , we get,

$\frac{3x^2(x+5)+17(x+5)-82}{x+5}$

On solving , we get,

$\frac{3x^3+15x^2+17x+85-82}{x+5}$

On simplifying, we get,

$\frac{3x^3+15x^2+17x+3}{x+5}$

Which is equal to the given expression.

Thus, option (c) is correct,

$3x^2+17-\frac{82}{x+5}$ is the equivalent fraction to the given expression $\frac{3x^3+15x^2+17x+3}{x+5}$