Question

Which expression is equivalent to?

Answer 1

Answer:

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

Step-by-step explanation:

$\frac{(-7m^4+15m^3-12m^2)+(3m^5-12m^4-7m^3)}{m-6}$

so simplify this expression we combine like terms

$\frac{-7m^4+15m^3-12m^2+3m^5-12m^4-7m^3}{m-6}$

$\frac{3m^5-19m^4+8m^3-12m^2}{m-6}$

now we factor out GCF m^2

$\frac{m^2(3m^3-19m^2+8m-12)}{m-6}$

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

$\frac{m^2(3m^3-19m^2+8m-12)}{m-6}$

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

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