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together. Examples: Factor each polynomial by group xy-5y-2x+10

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together.
Examples: Factor each polynomial by group
xy-5y-2x+10

together. Examples: Factor each polynomial by group xy-5y-2x+10

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GabrielProfissional · Tutor por 6 anos

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To factor the polynomial \(xy - 5y - 2x + 10\) by grouping, follow these steps:<br /><br />1. **Group the terms in pairs:**<br /> \[<br /> (xy - 5y) + (-2x + 10)<br /> \]<br /><br />2. **Factor out the greatest common factor (GCF) from each pair:**<br /> - From the first group \((xy - 5y)\), factor out \(y\):<br /> \[<br /> y(x - 5)<br /> \]<br /> - From the second group \((-2x + 10)\), factor out \(-2\):<br /> \[<br /> -2(x - 5)<br /> \]<br /><br />3. **Rewrite the expression using the factored groups:**<br /> \[<br /> y(x - 5) - 2(x - 5)<br /> \]<br /><br />4. **Factor out the common binomial factor \((x - 5)\): \[<br /> (x - 5)(y - 2)<br /> \]<br /><br />So, the factored form of the polynomial \(xy - 5y - 2x + 10\) is:<br />\[<br />(x - 5)(y - 2)<br />\]
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