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

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

Rewrite  g(x)  as

(-6x^3 + 5x^2  - 4x  +  3)

Note  that  if  f(x)  + cg(x)   results  in a polynomial of degree 2.......we  need to find c  such that

4x^3  + c( -6x^3)  =    0

So....this implies  that

4  - 6c   =   0

4   =  6c

c =  4/6  =   2/3