¿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 la expresión que, al multiplicarse, resulta en el polinomio original.
Answer
$(x)(x+3y)$
Answer for screen readers
d) $(x)(x+3y)$
Steps to Solve
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Identify the common factor Both terms in the polynomial $x^2 + 3xy$ have a common factor of $x$.
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Factor out the common factor Factor out $x$ from the polynomial: $x^2 + 3xy = x(x + 3y)$
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Verify the answer Distribute the $x$ back into the parentheses to check if it matches the original polynomial: $x(x + 3y) = x^2 + 3xy$
d) $(x)(x+3y)$
More Information
Factoring is the reverse process of expanding. We look for common terms to simplify algebraic expressions.
Tips
A common mistake is not factoring completely. For example, one might identify a common factor but not extract it correctly from all terms. Another mistake is incorrectly applying the distributive property when verifying the factored expression.
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