Factoring the expression x² + 7x + 8 involves finding two numbers that multiply to the constant term (8) and add up to the linear coefficient (7). Let’s break it down step-by-step:
- We start with the expression: x² + 7x + 8.
- Next, we look for two numbers that multiply to 8 and add to 7. Those two numbers are 1 and 8.
- Now, we can rewrite the quadratic expression in factored form: (x + 1)(x + 8).
So, the factored form of the expression x² + 7x + 8 is (x + 1)(x + 8).
This means that if you were to expand (x + 1)(x + 8), you would get back the original expression x² + 7x + 8. Factoring helps in understanding the roots of the equation as well, where the solutions for x are -1 and -8.
Understanding how to factor quadratic expressions like this one is a valuable skill in algebra, essential for solving equations and graphing quadratic functions!