Question

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

blank xexponent2+blank x+blank

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 the terms:

\[
6x^2 + 12x - 2x - 4
\]

Combine the like terms (\(12x\) and \(-2x\)):

\[
6x^2 + (12x - 2x) - 4 = 6x^2 + 10x - 4
\]

So the final answer is:

\[
6x^2 + 10x - 4
\]

In the blanks, we have:
- Blank for \(x^2\): **6**
- Blank for \(x\): **10**
- Blank for the constant: **-4**

Thus, filling in the blanks gives:

6 x^2 + 10 x + (-4)