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

Question
Polynomial factorization
asked 2021-02-11
Solve the following equation by factoring
\(\displaystyle{z}^{{2}}={8}{z}\)

Answers (1)

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
Final answer:
therefore, by factorization the solution of the equation \(\displaystyle{z}^{{2}}={8}{z}\) is:
z=0 or z =8
0

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