In Exercises 1–68, factor completely, or state that the polynomial is prime. x²y − 16y + 32 − 2x²

Factoring polynomials involves rewriting a polynomial expression as a product of simpler polynomials. This process is essential for simplifying expressions and solving equations. Common techniques include factoring out the greatest common factor, using special products like the difference of squares, and applying the quadratic formula when necessary.

A polynomial is considered prime if it cannot be factored into the product of two non-constant polynomials with real coefficients. Recognizing prime polynomials is crucial in algebra, as it helps determine the limits of simplification and the methods needed for solving polynomial equations.

Combining like terms is the process of simplifying an expression by adding or subtracting terms that have the same variable raised to the same power. This step is often necessary before factoring, as it helps to organize the polynomial into a standard form, making it easier to identify potential factors.