To rewrite x² + 5x + 6 as x² + rx + sx + 6, we need to factor the middle term (5x) in a way that allows us to split it into two terms that fit the desired form.
1. Start by factoring the coefficient of x², which is 1. Since 1 only has one pair of factors (1 and 1), we can rewrite x² as x².
2. Look at the coefficient of x, which is 5. We need to find two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of x). The two numbers are 2 and 3 because 2 * 3 = 6 and 2 + 3 = 5.
3. Now, rewrite 5x as 2x + 3x, so the expression becomes x² + 2x + 3x + 6.
Therefore, x² + 5x + 6 can be rewritten as x² + 2x + 3x + 6 in the desired form x² + rx + sx + 6.
