If \(x + 7\) is a factor of \(f(x)\), then \(f(-7) = 0\). This means that \(-7\) is a root of the polynomial, making \(f(-7)\) equal to zero. The factorization reveals that \((x + 7)\) is a linear factor of \(f(x)\), aiding in graphing and understanding the polynomial's properties.
If \(x + 7\) is a factor of \(f(x)\), it implies that \(f(-7) = 0\), based on the factor theorem. When \(x + 7\) is substituted into \(f(x)\), the result is zero, indicating that \(-7\) is a root of the polynomial. This means that when \(x = -7\), the polynomial \(f(x)\) evaluates to zero. Consequently, \(f(-7)\) represents a point on the graph where the polynomial intersects the x-axis.
Moreover, \(x + 7\) being a factor provides information about the factorization of \(f(x)\). It suggests that \((x + 7)\) is one of the linear factors contributing to the polynomial. Knowledge of \(f(-7) = 0\) and the factorization is crucial for understanding the behavior of the polynomial, aiding in graphing and analysis of its properties.