Solving for a:
2a\(x^{4}\)+\(x^{3}\)-bx+5 = 4\(x^{4}\)+\(x^{3}\)-c\(x^{2}\)+2x+5
Subtract 5 and \(x^{3}\) from both sides:
2a\(x^{4}\)-bx=4\(x^{4}\)-c\(x^{2}\)+2x
Add bx to both sides:
2a\(x^{4}\)=4\(x^{4}\)-c\(x^{2}\)+2x+bx
Divide both sides by 2\(x^{4}\):
a = 4\(x^{4}\)-c\(x^{2}\)+2x+bx/2\(x^{4}\)
Simplify:
a = 4\(x^{3}\)-cx+2+b/2\(x^{3}\)
Solving for b:
Begin by doing the same as for a by subtracting 5 and \(x^{3}\) from both sides. Again add bx to both sides to avoid having to work with negatives. You should now have 2a\(x^{4}\)=4\(x^{4}\)-c\(x^{2}\)+2x+bx.
Subtract 4\(x^{4}\) and 2x from both sides as well as adding c\(x^{2}\) to both sides:
2a\(x^{4}\)-4\(x^{4}\)+c\(x^{2}\)-2x=bx
Divide both sides by x:
b = 2a\(x^{4}\)-4\(x^{4}\)+c\(x^{2}\)-2x/x
Simplify:
b = 2a\(x^{3}\)-4\(x^{3}\)+cx-2
Solve for c:
Begin again by subtracting 5 and \(x^{3}\) from both sides. Next add c\(x^{2}\) to both sides to again avoid working with negatives:
2a\(x^{4}\)-bx+c\(x^{2}\)=4\(x^{4}\)+2x
Subtract 2a\(x^{4}\) and add bx to both sides:
c\(x^{2}\)=4\(x^{4}\)+2x-2a\(x^{4}\)+bx
Divide both sides by \(x^{2}\):
c = 4\(x^{4}\)+2x-2a\(x^{4}\)+bx/\(x^{2}\)
Simplify:
c = 4\(x^{3}\)+2-2a\(x^{3}\)+b/x
