To factor the expression x² + 2x – 3, we need to find two numbers that multiply to give the constant term (-3) and add up to give the coefficient of the linear term (2).
1. **Identify the product and sum**: We want two numbers that multiply to -3 (the constant term) and add up to 2 (the coefficient of x). The numbers that satisfy this condition are 3 and -1 because:
- 3 * (-1) = -3
- 3 + (-1) = 2
2. **Rewrite the middle term**: We can rewrite the expression by splitting the middle term using the two numbers we found:
x² + 3x – 1x – 3
3. **Group the terms**: Next, group the terms into two parts:
(x² + 3x) + (-1x – 3)
4. **Factor by grouping**: Now, factor out the common factors in each group:
x(x + 3) – 1(x + 3)
5. **Combine the factors**: We can see that (x + 3) is a common factor. So, we factor that out:
(x – 1)(x + 3)
Thus, the expression x² + 2x – 3 factors to (x – 1)(x + 3).