Factorize \(m^3 - 2m^2\) - 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)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
\(m^3 - 2m^2\) - m + 2
Let f(m) = \(m^3 - 2m^2\) - m + 2
= f(1)
= 1 - 2 - 1 + 2 = 0
∴ m - 1 is factor \(\frac{m^3 - 2m^2 - m + 2}{m - 1}\)
= \(m^2\) - m - 2
= (\(m^2\) - 2m + m - 2)
= m(m - 2) + 1(m - 2)
= ( m + 1)( m - 2)
= (m - 1)(m + 1)(m - 2)
Source: Myschool Past Questions Archive (Record #31404)