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Consider the polynomials f(x)=1-12x+3x^2-4x^3+6x^4 and g(x)=3-2x-6x^3+9x^4.

 

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

 May 25, 2021
 #1
avatar+1786 
+2

Since right now, f(x) has a degree of 4, (6x^4), cg(x) needs to have -6x^4 to balance it out. 

g(x) already has 9x^4, but it needs to be -6x^4, so you multiply by -2/3.

 

=^._.^=

 May 25, 2021
 #2
avatar+119816 
+2

Yeah....that  would  have been my guess too, catmg

 

But....look  what happens

 

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

 

3x^2  -  (32/3)x -  1

 

We  cancel  the x^4  and x^3   terms

 

So....I don't believe  there is  a  "c"  that  we  can find to  leave a 3rd power polynomial

 

 

cool cool cool

 May 25, 2021
 #3
avatar+1786 
+2

Oh no, it does say that c is a polynomial, so maybe c isn't a number?

 

=^._.^=

catmg  May 25, 2021

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