Question

find the lcm and hcf of (m^2-2m-15),(m^3-125-15m^2+75m)and (m^2-125)form division method​

Answer 1

find the lcm and hcf of (m^2-2m-15),(m^3-125-15m^2+75m)and (m^2-125)form division method

correction m^2 -125 is m^2-25

${m}^{2} - 2m - 15 \\ = {m}^{2} - 5m + 3m - 15 \\ = m(m - 5) + 3(m - 5) \\ = (m + 3)(m - 5)$

${m}^{3} - 125 - 15 {m}^{2} + 75m \\ = (m - 5)( {m}^{2} + 25 + 5m) - 15m(m - 5) \\ = (m - 5)( {m}^{2} - 10m + 25) \\ = (m - 5)( {m}^{2} - 5m - 5m + 25) \\ = (m - 5)(m - 5)(m - 5)$

${m}^{2} - 25 \\ (m + 5)(m - 5)$

HCF = m-5

LCM = (m+3)(m-5)(m-5)(m-5)(m+5)