Domanda del libro di testo
In Exercises 23–34, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial.
24. x² + 4x
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0. Review of Algebra
Factoring Polynomials
1:53 minutiProblema 25
Domanda del libro di testo
In Exercises 23–34, factor out the negative of the greatest common factor. −8x − 48
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Identify the greatest common factor (GCF) of the terms in the expression \(-8x - 48\).
The GCF of \(-8x\) and \(-48\) is \(8\).
Factor out the negative of the GCF, which is \(-8\), from each term in the expression.
Rewrite the expression as \(-8(x + 6)\).
Verify the factorization by distributing \(-8\) back into the expression to ensure it equals the original expression.
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Greatest Common Factor (GCF)
The Greatest Common Factor is the largest integer that divides two or more numbers without leaving a remainder. To find the GCF, one can list the factors of each number and identify the highest one. In the expression −8x − 48, the GCF is 8, as both terms can be divided by 8.
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Graphs of Common Functions
Factoring
Factoring is the process of breaking down an expression into simpler components, or factors, that when multiplied together yield the original expression. In this case, factoring out the GCF involves rewriting the expression in a way that highlights the common factor, making it easier to simplify or solve.
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Negative Factor
Factoring out a negative involves taking the negative of the GCF and using it to rewrite the expression. This is important for maintaining the sign of the original expression. In the given problem, factoring out -8 from −8x − 48 results in -8(x + 6), which simplifies the expression while keeping its value intact.
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