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Find h(x), with terms in order of decreasing degree, if \(3x^4+2x-1+h(x)=5x^2-6x-1.\)

 Oct 15, 2019
 #1
avatar+104969 
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Not too bad.....

 

We need to figure this

 

    3x^4  + 2x  + 1

+     h(x)

______________

  5x^2  - 6x - 1

 

Note that the first term of h(x)  must have been     -3x^4   since there is no fourth power term in the final result

The second term must have been  5x^2

The third term must have been    2x + ax = - 6x  ....so  ax  = -8x

And the last term must have been -1 + k = -1    ⇒  k  = 0

 

So  h(x)  must have been     -3x^4  + 5x^2  - 8x  

 

Check :

 

3x^4  +  0x^2   +  2x   -  1

-3x^4 +  5x^2   -  8x    + 0

_____________________

             5x^2   -  6x   - 1

 

 

cool cool cool

 Oct 15, 2019

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