To determine a factor of the expression x² + 8x + 48, we can start by trying to factor it into two binomials. The standard approach is to look for two numbers that multiply to the constant term (48) and add to the coefficient of the linear term (8).
In this case, we need to find two numbers that multiply to 48 and add up to 8. After testing some pairs of factors of 48, we find that 6 and 8 work because:
- 6 × 8 = 48
- 6 + 8 = 14
Since we cannot find two such numbers that fit both criteria directly, we must check whether the expression is factorable or not. In this case, we can also use the quadratic formula, but considering the factors of the constant term and checking integer values can also help.
However, we can confirm that the expression cannot be factored into simpler integer binomials directly due to the nature of its components. Thus, the expression x² + 8x + 48 does not have simple integer factors.
To summarize, while we cannot find simple factors that neatly fit the criteria, it’s essential to verify and explore various means of sorting through polynomial expressions to understand their factorization better. The potential candidates for higher-order polynomial factors or evaluating via the quadratic formula can provide further insights.