Pregunta
Factor the given polynomial by finding the greatest common monomial factor (or the negative of the greatest common monomial \[ 6 x^{3} y+2 x y^{3}-26 x y \]
Ask by Chang Christensen. in the United States
Feb 20,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The greatest common monomial factor is \(2xy\), and the factored form is \(2xy(3x^{2}+y^{2}-13)\).
Solución
Factor the expression \( 6x^3y+2xy^3-26xy \).
Factor the expression by following steps:
- step0: Factor:
\(6x^{3}y+2xy^{3}-26xy\)
- step1: Rewrite the expression:
\(2xy\times 3x^{2}+2xy\times y^{2}-2xy\times 13\)
- step2: Factor the expression:
\(2xy\left(3x^{2}+y^{2}-13\right)\)
The greatest common monomial factor of the given polynomial \(6x^{3}y+2xy^{3}-26xy\) is \(2xy\), and the factored form is \(2xy(3x^{2}+y^{2}-13)\).
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Simplifique esta solución Beyond the Answer
To factor the polynomial \( 6 x^{3} y + 2 x y^{3} - 26 x y \), start by identifying the greatest common monomial factor (GCF) of the terms. The coefficients 6, 2, and -26 have a GCF of 2. The variable factors include \( x \) and \( y \); the lowest powers of \( x \) and \( y \) across all terms are \( x^1 \) and \( y^1 \), respectively. Therefore, the GCF of the entire expression is \( 2xy \). Now, factor out \( 2xy \) from each term: \[ 6 x^{3} y + 2 x y^{3} - 26 x y = 2xy(3x^{2} + y^{2} - 13). \] Now the polynomial has been factored into \( 2xy(3x^{2}+y^{2}-13) \).
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