1. The problem is to understand and analyze the given polynomial expressions: $x^3 - 3x + 4$, $4x^2 - 2y + 7$, and $-x^2 + 5x - 2$. 2. These are polynomial expressions in variables $x$ and $y$. The first and third are univariate polynomials in $x$, and the second is a bivariate polynomial in $x$ and $y$. 3. For the first polynomial $x^3 - 3x + 4$, it is a cubic polynomial. Important rules include the degree (3), leading coefficient (1), and constant term (4). 4. For the second polynomial $4x^2 - 2y + 7$, it is quadratic in $x$ and linear in $y$. It cannot be simplified further without values for $x$ or $y$. 5. For the third polynomial $-x^2 + 5x - 2$, it is quadratic in $x$ with leading coefficient $-1$. 6. No further simplification or factorization is possible without additional context or instructions. Final answer: The expressions are correctly written polynomials with no simplification needed.