# Solve the following equation by factoring z^2=8 z

Question
Polynomial factorization
Solve the following equation by factoring
$$\displaystyle{z}^{{2}}={8}{z}$$

2021-02-12
Concept:
Factorization is the process of breaking a polynomial into product of its factors.
For example: if a quadratic equation $$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}$$ has roots p and q then in factor form it can be written as (x-p)(x-q)=0
Solution:
$$\displaystyle{z}^{{2}}={8}{z}$$
subtract 8z from both sides:
$$\displaystyle{z}^{{2}}-{8}{z}={8}{z}-{8}{z}$$
$$\displaystyle{z}^{{2}}-{8}{z}={0}$$
tale out z as it is common to both:
z(z-8)=0
now, the above expression shows that we have broken the given expression in to it's factors, z=0 or (z-8)=0
z=0 or z=8
therefore, by factorization the solution of the equation $$\displaystyle{z}^{{2}}={8}{z}$$ is:
z=0 or z =8

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