¿Cuál es el resultado de factorizar el siguiente polinomio x² + 3xy?
Understand the Problem
La pregunta pide encontrar el resultado de factorizar el polinomio x² + 3xy. Esto implica encontrar los factores comunes en los términos del polinomio y expresarlo como un producto de esos factores.
Answer
$x(x + 3y)$
Answer for screen readers
$x(x + 3y)$
Steps to Solve
- Identify the terms in the polynomial
The polynomial given is $x^2 + 3xy$. It has two terms: $x^2$ and $3xy$.
- Find the greatest common factor (GCF)
The GCF of $x^2$ and $3xy$ is $x$ because $x^2 = x \cdot x$ and $3xy = 3 \cdot x \cdot y$. $x$ is the only factor that appears in both terms.
- Factor out the GCF
Factor out $x$ from both terms: $x^2 + 3xy = x(x + 3y)$
- Final Answer
The factored form of the polynomial is $x(x + 3y)$.
$x(x + 3y)$
More Information
Factoring is the reverse process of distribution. We are undoing the multiplication to find the original factors.
Tips
A common mistake is to not factor completely. Ensure you've found the greatest common factor, not just a common factor. Another mistake is to forget to include the remaining terms inside the parentheses after factoring out the GCF. For example, factoring out only the x and leaving $x + 3xy$ instead of $x(x+3y)$.
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