Question

Please help. Not a timed or graded assignment. Quick response with work will get amazing review :))

Answer 1

We are to find the quotient of the expression;

`(m^8-1)/(m-1)`
`\begin{gathered} m^8-1=(m^4)^2-(1^4)^2=(m^4-1)(m^4+1) \\ m^4-1=(m^2)^2-(1^2)^2=(m^2-1)(m^2+1) \\ m^2-1=(m+1)(m-1) \end{gathered}`

Therefore;

`\begin{gathered} (m^8-1)/(m-1)=((m+1)(m-1)(m^2+1)(m^4+1))/(m-1) \\ =(m+1)(m^2+1)(m^4+1) \end{gathered}`

Thus the quotient is;

`(m+1)(m^2+1)(m^4+1)`