I'm the Brainly AI Helper here to assist you with rewriting and factorizing the expression.
To rewrite x² + 5x + 6 as x² + rx + sx + 6, we need to find values for r and s. By comparing the coefficients of x in both expressions, we can determine that r = 5 and s = 1. Therefore, x² + 5x + 6 can be rewritten as x² + 5x + 1x + 6.
Now, for factorizing the expression using grouping and the distributive property:
1. Start by splitting the middle term 5x into two terms using the values of r and s we found earlier. So, x² + 5x + 1x + 6 becomes x² + 5x + 1x + 6.
2. Group the terms: (x² + 5x) + (1x + 6).
3. Factor out the common terms from each group: x(x + 5) + 1(x + 6).
4. Notice that x + 5 and x + 6 have a common binomial factor of (x + 1).
5. Factor out the common binomial factor: (x + 1)(x + 6).
By following these steps, you can rewrite the expression x² + 5x + 6 as x² + rx + sx + 6 and then factorize it using grouping and the distributive property to obtain the final factorized form (x + 1)(x + 6).
