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Multiply the polynomials (3x−1)(2x+4)

.(2 points)
x2+
x+

1 answer

To multiply the polynomials \((3x - 1)(2x + 4)\), we can use the distributive property (also known as the FOIL method for binomials).

  1. First, multiply the first terms: \[ 3x \cdot 2x = 6x^2 \]

  2. Next, multiply the outer terms: \[ 3x \cdot 4 = 12x \]

  3. Then, multiply the inner terms: \[ -1 \cdot 2x = -2x \]

  4. Finally, multiply the last terms: \[ -1 \cdot 4 = -4 \]

Now, we combine all these results: \[ 6x^2 + 12x - 2x - 4 \]

Combine the like terms (\(12x\) and \(-2x\)): \[ 6x^2 + 10x - 4 \]

So, the resulting polynomial is: \[ 6x^2 + 10x - 4 \]

Putting it in the format you requested: \[ x^2 + 10x + (-4) \]

Final answer: \[ 6x^2 + 10x - 4 \]