Pergunta

Factor the polynomial completely y(y-6)+5(y-6)^2 y(y-6)+5(y-6)^2=(y-6)(y+10) (Type your answer in factored form.) x That's incorrect. Identify the greatest common factor (GCF) and rewrite each term as the product of the GCF and the remaining factor. Then use the distributive property to factor out the GCF After factoring out the GCF the remaining terms should be simplified and factored if possible. Check your work carefully.
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MarcioProfissional · Tutor por 6 anos
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To factor the polynomial \( y(y-6) + 5(y-6)^2 \) completely, let's follow these steps:<br /><br />1. **Identify the Greatest Common Factor (GCF):**<br /><br /> Notice that both terms in the expression have a common factor of \( (y-6) \).<br /><br />2. **Rewrite Each Term Using the GCF:**<br /><br /> - The first term \( y(y-6) \) can be rewritten as \( (y-6)y \).<br /> - The second term \( 5(y-6)^2 \) is already expressed with \( (y-6) \) as a factor.<br /><br />3. **Factor Out the GCF:**<br /><br /> Factor out the common factor \( (y-6) \) from each term:<br /><br /> \[<br /> y(y-6) + 5(y-6)^2 = (y-6)(y) + (y-6)(5(y-6))<br /> \]<br /><br /> \[<br /> = (y-6)(y + 5(y-6))<br /> \]<br /><br />4. **Simplify the Remaining Terms:**<br /><br /> Simplify the expression inside the parentheses:<br /><br /> \[<br /> y + 5(y-6) = y + 5y - 30 = 6y - 30<br /> \]<br /><br />5. **Write the Factored Form:**<br /><br /> Substitute back into the factored expression:<br /><br /> \[<br /> (y-6)(6y - 30)<br /> \]<br /><br />6. **Further Factor if Possible:**<br /><br /> Notice that \( 6y - 30 \) has a common factor of 6:<br /><br /> \[<br /> 6y - 30 = 6(y - 5)<br /> \]<br /><br /> Substitute this back into the expression:<br /><br /> \[<br /> (y-6)(6(y-5)) = 6(y-6)(y-5)<br /> \]<br /><br />Thus, the completely factored form of the polynomial is:<br /><br />\[<br />6(y-6)(y-5)<br />\]
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