MATHEMATICS

JAMB 2022 - Question 26

Mathematics 2022 JAMB Past Questions - Question 26: Factorize m3 – m2 – m + 2

Factorize m3 – m2 – m + 2
A:
B:
C:
D:
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Correct Answer

C

Explanation

To factorize the expression m^3 - m^2 - m + 2, we can look for common factors and then use factoring techniques.First, we can observe that all the terms have a common factor of 1. So, we can factor out 1:m^3 - m^2 - m + 2 = 1 * (m^3 - m^2 - m + 2)Next, we can try to factor the expression inside the parentheses. By grouping, we can rewrite the expression as:(m^3 - m^2) - (m - 2)Now, we can factor out common terms from each group:m^2(m - 1) - 1(m - 2)Finally, we can factor out the common factor of (m - 1):(m - 1)(m^2 - 1) - (m - 2)Now, we can further factor the difference of squares:(m - 1)(m + 1)(m - 1) - (m - 2)Simplifying, we get:(m - 1)^2(m + 1) - (m - 2)Therefore, the expression m^3 - m^2 - m + 2 can be factorized as (m - 1)^2(m + 1) - (m - 2).

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