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Factorize \(m^3 - 2m^2\) - m + 2

Mathematics
JAMB 1991

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)
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Correct Answer: Option C
Explanation

\(m^3 - 2m^2\) - 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)


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