To determine which polynomial divides evenly by \( x + 3 \), we can perform polynomial long division on each polynomial provided. However, since you haven't listed the specific polynomials you're interested in, I can explain the process of long division with a general example.
Here's how to use long division to check if a polynomial \( P(x) \) is divisible by \( D(x) = x + 3 \):
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Set Up the Division: Write \( P(x) \) under the long division bar and \( D(x) = x + 3 \) outside.
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Divide: Divide the leading term of \( P(x) \) by the leading term of \( D(x) \). This will give you the first term of the quotient.
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Multiply: Multiply \( D(x) \) by this new term and write the result under \( P(x) \).
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Subtract: Subtract this result from \( P(x) \). Bring down any remaining terms.
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Repeat: Repeat steps 2-4 with the new polynomial formed from the subtraction until the degree of the new polynomial (the remainder) is less than the degree of \( D(x) \).
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Check Remainder: If the remainder is 0, then \( P(x) \) is divisible by \( D(x) = x + 3 \). If the remainder is non-zero, it is not divisible.
If you give me the specific polynomials you're considering, I can apply this process to those polynomials. Let me know if you would like that!
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