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