How do you Factor fourth degree polynomial?

Answer 1

There is no simple way.

A polynomial of the form f(x) = ax4 + bx3 + cx2 + dx + e may have four real factors: it may have none. Binomial factors will be of the form px + q, where p is one of the factors of a and q is one of the factors of e. In general, p and q can be positive or negative. That gives a very large number of possible binomial factors of the polynomial.

Evaluate f(x) for x = -q/p, that is, substitute x = -q/p in the polynomial and calculate its value. If f(-q/p) = 0 then (x + q/p) = (px + q) is a factor.

It may be possible to find the zeros of the quadratic by numerical or graphical methods. If x = z if a root then (x + z) is a factor.

If the four factors are

(x - s), (x - t), (x - u) and (x - v) then

s+t+u+v = b/a

st +su+ sv + tu + tv +uv = c/a

stu + stv + suv + tuv = d/a

and stuv = e/a

One option is to solve these equations simultaneously for s, t, u and v.