Rational Root Theorem:
If the rational number [tex]x=\frac{b}{c}[/tex] is a zero of a higher degree polynomial:
[tex]P(x)=kx^{n}+...+m[/tex]
where all the coefficients are integers. Then [tex]b[/tex] will be a factor of [tex]m[/tex] and [tex]c[/tex] will be a factor of [tex]k[/tex]
1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial [tex]P(x)[/tex]
2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is [tex]x=r[/tex]. It will be a zero if [tex]P(r)=0[/tex]. Then if this is true, write the polynomial as:
[tex]P(x)=(x-r)Q(x)[/tex]
3. Repeat this process using [tex]Q(x)[/tex] this time rather than [tex]P(x)[/tex]. The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.
