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Consider the polynomial f(x) = 1 - 12x + 3x^2 - 4x^3 + 5x^4 and g(x) = 3 - 2x - 6x^3 + 19x^4.  Find c such that the polynomial f(x) + cg(x) has degree 3.

 Jun 27, 2021
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We need to have the x^4 terms 'cancel out' to end with a degree 3 polynomial

 

c * 5x^4   + 19x^4 = 0

c = - 19/5

 

 

so    the polynomial could be anything with   -19/5  x^4  in it     ( and no higher degree term in it...and also, don't 'cancel out the x^3 terms)

 

      - 19/5 x^4   + x^3   - x^2 + 4 x  + 10      would be an example....

 Jun 27, 2021
edited by Guest  Jun 27, 2021
edited by ElectricPavlov  Jun 27, 2021

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