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gizmo_the_mogwai [7]
3 years ago
5

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 sol

ve this sum it is urgent 5 points on it please
Mathematics
1 answer:
Marianna [84]3 years ago
8 0

Answer:  5x + 15

<u>Step-by-step explanation:</u>

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

Let k represent the unknown number.

         <u>   x  + 4                        </u>

x² + 5 ) x³ + 4x² + 0x + 5+k

         - <u>(x³          + 5x)</u>

                   4x²  -  5x  +  5+k

               -  <u>(4x²           +    20)</u>

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              <em>subtracted 4x² from both sides</em>

                5 + k = 5x + 20      <em>added 5x to both sides</em>      

                     k  = 5x + 15        <em>subtracted 5 from both sides</em>    

     

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