factorize m$^3$ - m$^2$ + 2m - 2

1. Analyze the question

We are asked to factorize the polynomial expression: m³ - m² + 2m - 2. This is a four-term expression, which suggests that factorization by grouping is the most effective method.

2. Explain the concept

Factorization by grouping involves splitting the expression into two pairs of terms. We look for a common factor in each pair. Once we factor out the common terms, we look for a common binomial factor that can be pulled out to complete the factorization.

3. Show the solution

Step 1: Group the terms into two pairs. (m³ - m²) + (2m - 2)

Step 2: Factor out the greatest common factor (GCF) from each group.

• In the first group (m³ - m²), the GCF is m². m²(m - 1)
• In the second group (2m - 2), the GCF is 2. 2(m - 1)

Step 3: Rewrite the expression with the factored groups. m²(m - 1) + 2(m - 1)

Step 4: Factor out the common binomial (m - 1). Since (m - 1) appears in both parts, we can factor it out: (m - 1)(m² + 2)

4. Identify the answer

Comparing our result, (m - 1)(m² + 2), to the provided options, we see that it matches option D.

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5. Tip

When you see a polynomial with four terms in a JAMB exam, always try grouping the first two and the last two terms first. If the terms inside the brackets after the first step are identical, you are on the right track! If they aren't, try rearranging the terms before grouping.