Domanda del libro di testo
Factor out the greatest common factor from each polynomial. See Example 1. 5(a+3)3-2(a+3)+(a+3)2
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0. Review of Algebra
Factoring Polynomials
2:02 minutiProblema 27
Domanda del libro di testo
In Exercises 23–34, factor out the negative of the greatest common factor. −2x² + 6x − 14
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Identify the greatest common factor (GCF) of the terms in the expression \(-2x^2 + 6x - 14\).
The GCF of the coefficients \(-2\), \(6\), and \(-14\) is \(2\).
Factor out \(-2\) from each term in the expression.
Rewrite the expression as \(-2(x^2 - 3x + 7)\).
Verify by distributing \(-2\) back through the expression to ensure it matches the original expression.
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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.
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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.
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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.
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