\( y^{3}+3 y^{2}-y+5 \) as \( y=-1 \)

To evaluate the polynomial \( y^{3}+3y^{2}-y+5 \) at \( y=-1 \), we can simply substitute \(-1\) into the equation. Calculating, we have: \[ (-1)^3 + 3(-1)^2 - (-1) + 5 = -1 + 3 + 1 + 5 = 8. \] So, when \( y = -1 \), the polynomial evaluates to \( 8 \). In polynomial evaluations, substituting numbers directly can frequently reveal insights about the polynomial’s behavior at those points. It’s a way to see how values change and can even help identify potential roots! When working with higher-degree polynomials, always consider using synthetic division for efficiency when checking values closer to potential roots. This technique allows one to find remainders quickly, potentially simplifying the problem-solving process!