To multiply the polynomials \( (3x - 1)(2x + 4) \), you can use the distributive property (also known as the FOIL method for binomials):
\[ (3x - 1)(2x + 4) = 3x \cdot 2x + 3x \cdot 4 - 1 \cdot 2x - 1 \cdot 4 \]
Now, calculate each term:
- \( 3x \cdot 2x = 6x^2 \)
- \( 3x \cdot 4 = 12x \)
- \( -1 \cdot 2x = -2x \)
- \( -1 \cdot 4 = -4 \)
Now, combine the like terms \( 12x \) and \( -2x \):
\[ 6x^2 + (12x - 2x) - 4 = 6x^2 + 10x - 4 \]
Thus, the product of the polynomials is:
\[ \boxed{6x^2 + 10x - 4} \]
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