Question

Explain one of the theorems that you would use to find the zero of higher degree polynomial

Answer 1

Rational Root Theorem:

If the rational number $x=\frac{b}{c}$ is a zero of a higher degree polynomial:

$P(x)=kx^{n}+...+m$

where all the coefficients are integers. Then $b$ will be a factor of $m$ and $c$ will be a factor of $k$

1. Use the rational root theorem to enumerate all possible rational zeroes of the polynomial $P(x)$

2. Evaluate the polynomial from the first step until you can find a zero. Let’s suppose the zero is $x=r$. It will be a zero if $P(r)=0$. Then if this is true, write the polynomial as:

$P(x)=(x-r)Q(x)$

3. Repeat this process using $Q(x)$ this time rather than $P(x)$. The process finishes until we reach a second degree polynomial, then solve as it is widely known for a quadratic equation.