Question

Find the H.C.F. of $(6m^3-17m^2-5m+6)$ and $(6m^3-5m^2-3m+2)$ by using the division method.

• A. $6m^2+m-2$
  
• B. $6m^2+m+2$
• C. $6m^2-m-2$
• D. $6m^2-m+2$

Answer 1

The correct option is A $6m^2+m-2$


$6m^3-17m^2-5m+6)6m^3-5m^2-3m+2(16m^3-17m^2-5m+6\underset{–}{-+-+}12m^2+2m-4$

$12m^2+2m-4=2(6m^2+m-2)$

$6m^2+m-2)6m^3-17m^2-5m+6(m-36m^3+m^2-2m\underset{–}{+-+}-18m^2-3m+6-18m^2-3m+6\underset{–}{++-}0$

Therefore, the H.C.F. of $(6m^3-17m^2-5m+6)$ and $(6m^3-5m^2-3m+2)=6m^2+m-2$