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 we do it step-by-step:
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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, we combine all these results: \[ 2x^2 - 8x + x - 4 \]
Next, combine the like terms (\(-8x\) and \(x\)): \[ 2x^2 - 7x - 4 \]
Thus, the product of the polynomials \( (2x + 1)(x - 4) \) is: \[ 2x^2 - 7x - 4 \]
In terms of the placeholders you provided \( \square x^2 + \square x + \square \), we can fill in the values as follows:
- First coefficient (for \(x^2\)): 2
- Second coefficient (for \(x\)): -7
- Constant term: -4
Final answer: \[ 2x^2 - 7x - 4 \]