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

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