In Exercises 23–34, factor out the negative of the greatest common factor.−5y² + 40x

Verified step by step guidance

1. Identify the greatest common factor (GCF) of the terms in the expression \(-5y^2 + 40x\).
2. The GCF of \(-5y^2\) and \(40x\) is \(5\).
3. Factor out the negative of the GCF, which is \(-5\), from each term in the expression.
4. Rewrite the expression as \(-5(y^2 - 8x)\).
5. Verify the factorization by distributing \(-5\) back into the expression to ensure it equals the original expression.

Key Concepts

Greatest Common Factor (GCF)

The Greatest Common Factor is the largest integer or algebraic expression that divides two or more terms without leaving a remainder. To find the GCF, identify the common factors of the coefficients and the variables in each term. In the expression −5y² + 40x, the GCF is 5, as it is the highest number that can evenly divide both coefficients.

Factoring

Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. This is essential in algebra for simplifying expressions and solving equations. In this case, factoring out the GCF helps to rewrite the expression in a more manageable form.

Negative Sign in Factoring

When factoring out a negative, it means that the GCF is taken as a negative value, which can change the signs of the terms in the expression. This is important for maintaining the equality of the expression. In the given problem, factoring out -5 from −5y² + 40x results in a positive expression, which can simplify further analysis or calculations.