To find the product of the polynomials \( (2x + 1)(x - 4) \), we can use the distributive property (also known as the FOIL method for binomials).
Here’s how to do it step by step:
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Distribute \( 2x \) to both terms in the second polynomial: \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-4) = -8x \]
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Distribute \( 1 \) to both terms in the second polynomial: \[ 1 \cdot x = x \] \[ 1 \cdot (-4) = -4 \]
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Now, combine all the results: \[ 2x^2 - 8x + x - 4 \]
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Combine like terms: \[ 2x^2 + (-8x + x) - 4 = 2x^2 - 7x - 4 \]
Thus, the product of the polynomials \( (2x + 1)(x - 4) \) is: \[ \boxed{2x^2 - 7x - 4} \]