To find the product of the polynomials \( (3x + 5)(2x - 7) \), we can use the distributive property (also known as the FOIL method for binomials).
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First: Multiply the first terms: \[ 3x \cdot 2x = 6x^2 \]
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Outer: Multiply the outer terms: \[ 3x \cdot (-7) = -21x \]
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Inner: Multiply the inner terms: \[ 5 \cdot 2x = 10x \]
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Last: Multiply the last terms: \[ 5 \cdot (-7) = -35 \]
Now, combine all the results: \[ 6x^2 - 21x + 10x - 35 \]
Next, combine the like terms (-21x and 10x): \[ 6x^2 - 11x - 35 \]
So, the product of the polynomials \( (3x + 5)(2x - 7) \) is: \[ \boxed{6x^2 - 11x - 35} \]
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