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Consider the polynomials

\[f(x)=1-12x+3x^2-4x^3+5x^4\]

and 

\[g(x)=3-2x-6x^3+9x^4.\]

Find $f(x)+cg(x)$ such that the polynomial  has degree 3.

 Feb 20, 2021
 #1
avatar+118069 
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f(x)   =   5x^4  -4x^3  +  3x^2   - 12x  + 1

 

g(x)   =   9x^4  - 6x^3  -  2x   +  3

 

Really    we  just  want to find  a  "c"   such  that

 

5x^4  +  c ( 9x^4)   =      0

 

So    getting  rid of  the  "x^4"  thingys    we  have

 

5  +  9c    =  0

 

9c    =   -  5

 

c  =  -5/9

 

Proof

 

5x^4  -4x^3  +  3x^2   - 12x  + 1  + (-5/9) [   9x^4  - 6x^3  -  2x   +  3]  =

 

-(2 x^3)/3 + 3 x^2 - (98 x)/9 - 2/3

 

cool cool cool

 Feb 20, 2021
edited by CPhill  Feb 20, 2021

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