Question

Not a graded or timed assessment. Need help, thank you. :)

Answer 1

We are given the following division problem

`(m^8-1)/(m-1)`

We need to factor out the numerator first

`m^8-1=(m^4)^2-1^2`

Apply the difference of squares formula

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

Again, factor out the term on the right side

`m^4-1=(m^2)^2-1^2`

Apply the difference of squares formula

`(m^2)^2-1^2=(m^2+1)(m^2-1)`

Again, factor out the term on the right side

`m^2-1=(m)^2-1^2`

Apply the difference of squares formula

`(m)^2-1^2=(m+1)(m-1)_{}`

Finally, the expression becomes

`(m^8-1)/(m-1)=((m^4+1)(m^2+1)(m+1)(m-1))/(m-1)`

(m-1) cancels out

`(m^8-1)/(m-1)=(m^4+1)(m^2+1)(m+1)`

Therefore, the quotient is

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

Or in simplified form

`m^7+m^6+m^5+m^4+m^3+m^2+m+1`