Multiply the polynomials (3x−1)(2x+4) .(2 points)

Question

x2+
x+

Answer 1

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

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

2. Multiply the outer terms: \[ 3x \cdot 4 = 12x \]

3. Multiply the inner terms: \[ -1 \cdot 2x = -2x \]

4. Multiply the last terms: \[ -1 \cdot 4 = -4 \]

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

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

Thus, the product of the polynomials \( (3x - 1)(2x + 4) \) is: \[ 6x^2 + 10x - 4 \]

So, the final answer is:

• \(x^2\) coefficient: 6
• \(x\) coefficient: 10
• Constant: -4

Therefore, you would fill in:

• \(x^2 + 10x - 4\)