Question

What should be added to x^3+4x^2+5, so that it is completely divisible by x^2+5? Here ^=power or exponent guys please please solve this sum it is urgent 5 points on it please

Answer 1

Answer:  5x + 15

Step-by-step explanation:

Divide (x² + 5) into (x³ + 4x² + 5) to see what is needed to make a remainder of zero.

Let k represent the unknown number.

            x  + 4                        

x² + 5 ) x³ + 4x² + 0x + 5+k

         - (x³          + 5x)

                   4x²  -  5x  +  5+k

               -  (4x²           +    20)

In order to have a remainder of zero, 4x² -5x + 5 + k must equal 4x² + 20

Solve for k:

4x² -5x + 5 + k = 4x² + 20

      -5x + 5 + k = 20              subtracted 4x² from both sides

                5 + k = 5x + 20      added 5x to both sides      

                     k  = 5x + 15        subtracted 5 from both sides