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

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Rational Root Theorem:


If the rational number
x=(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.


User Johannes Ewald
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