To multiply the polynomials \( (3x - 1)(2x + 4) \), we can use the distributive property (also known as the FOIL method for binomials).
Let's multiply them step-by-step:
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First: Multiply the first terms in each binomial: \[ 3x \cdot 2x = 6x^2 \]
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Outer: Multiply the outer terms: \[ 3x \cdot 4 = 12x \]
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Inner: Multiply the inner terms: \[ -1 \cdot 2x = -2x \]
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Last: Multiply the last terms: \[ -1 \cdot 4 = -4 \]
Now, combine all these results: \[ 6x^2 + 12x - 2x - 4 \]
Combine like terms (\(12x - 2x\)): \[ 6x^2 + 10x - 4 \]
So, the result of multiplying the polynomials \( (3x - 1)(2x + 4) \) is: \[ \boxed{6x^2 + 10x - 4} \]
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