In Exercises 23–34, factor out the negative of the greatest common factor. −2x² + 6x − 14

Key Concepts

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest integer or algebraic expression that divides each term of a polynomial without leaving a remainder. To find the GCF, identify the common factors of the coefficients and the variables in each term. In the expression −2x² + 6x − 14, the GCF is -2, as it is the highest factor that can be factored out from all terms.

Factoring Polynomials

Factoring polynomials involves rewriting a polynomial as a product of its factors. This process simplifies expressions and can help solve equations. In this case, factoring out the GCF allows us to express the polynomial in a simpler form, making it easier to analyze or solve. The goal is to express the polynomial in a way that highlights its structure.

Negative Sign in Factoring

Factoring out a negative sign means that we are extracting a negative value from the polynomial, which can change the signs of the terms. This is particularly useful when the leading coefficient is negative, as it can simplify the expression and make it easier to work with. In the given polynomial, factoring out -2 not only simplifies the expression but also ensures that the leading coefficient of the resulting polynomial is positive.