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

Question

()x^2+()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. First: Multiply the first terms: \[ 3x \cdot 2x = 6x^2 \]

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

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

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

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

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

So the final answer should be: \[ 6x^2 + 10x - 4 \]

Thus, the polynomial can be expressed as: \[ (6)x^2 + (10)x + (-4) \]

So, the coefficients are \(6\), \(10\), and \(-4\).