To find the product of the polynomials \( (2x + 1)(x - 4) \), we will apply the distributive property (also known as the FOIL method for binomials).
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Multiply the first terms: \[ 2x \cdot x = 2x^2 \]
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Multiply the outer terms: \[ 2x \cdot (-4) = -8x \]
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Multiply the inner terms: \[ 1 \cdot x = x \]
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Multiply the last terms: \[ 1 \cdot (-4) = -4 \]
Now combine all these results: \[ 2x^2 - 8x + x - 4 \] Combine the like terms (-8x and x): \[ 2x^2 - 7x - 4 \]
So, the product of the polynomials \( (2x + 1)(x - 4) \) is: \[ 2x^2 - 7x - 4 \]
Thus, the coefficients for your question will be:
- For the coefficient of \( x \): \(-7\)
- For the constant term: \(-4\)
Final answer: \[ 2x^2 - 7x - 4 \]
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