Consider the polynomials \(f(x)=1-12x+3x^2-4x^3+5x^4\) and \(g(x)=3-2x-6x^3+9x^4.\) Find c such that the polynomial\( f(x)+cg(x)\) has degree 3.
+26367 Consider the polynomials \(f(x)=1-12x+3x^2-4x^3+5x^4\) and \(g(x)=3-2x-6x^3+9x^4\).
Find \(c\) such that the polynomial \(f(x)+cg(x)\) has degree 3.
\(\begin{array}{|rcll|} \hline -5x^4 &=& c*9x^4 \\\\ c &=& -\dfrac{5x^4}{9x^4} \\\\ \mathbf{c} &=& \mathbf{-\dfrac{5 }{9}} \\ \hline \end{array}\)
