Factorize m3 - 2m2 - m 2 - JAMB Mathematics 1991 Question
Factorize m3 - 2m2 - m + 2
A
(m2 + 1)(m - 2)
B
(m - 1)(m + 1)(m + 2)
C
(m - 2)(m + 1)(m - 1)
D
(m2 + 2)(m - 1)
correct option: c
m3 - 2m2 - m + 2
Let f(m) = m3 - 2m2 - m2 + 2
= f(1)
= 1 - 2 - 2 + 2 = 0
∴ m - 1 is factor \(\frac{m^3 - 2m^2 - m^2 + 2}{m - 1}\)
= m2 - m - 2
= (m - 1)m2 - m - 2
= (m - 1)(m + 1)(m - 2)
Let f(m) = m3 - 2m2 - m2 + 2
= f(1)
= 1 - 2 - 2 + 2 = 0
∴ m - 1 is factor \(\frac{m^3 - 2m^2 - m^2 + 2}{m - 1}\)
= m2 - m - 2
= (m - 1)m2 - m - 2
= (m - 1)(m + 1)(m - 2)
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