Question

Which expression is equivalent to?

Answer 1

3m^4 - m^3 + 2m^2

Explanation:

`((-7m^4+15m^3-12m^2)+(3m^5-12m^4-7m^3))/(m-6)`

so simplify this expression we combine like terms

`(-7m^4+15m^3-12m^2+3m^5-12m^4-7m^3)/(m-6)`

`(3m^5-19m^4+8m^3-12m^2)/(m-6)`

now we factor out GCF m^2

`(m^2(3m^3-19m^2+8m-12))/(m-6)`

divide 3m^2-19m^2+8m-12 by m-6 using long division or synthetic division

6 3 -19 8 -12

0 18 -6 12

------------------------------------------

3 -1 2 0

So its 3m^2 -1m + 2

`(m^2(3m^3-19m^2+8m-12))/(m-6)`

m^2(3m^2-1m+2)

3m^4 - 1m^3 + 2m^2