Question

Multiply the polynomials (3x−1)(2x+4) .(2 points) x2+ x+

Answer 1

blankx^2+blankx+blank

Answer 2

To multiply the polynomials \((3x - 1)(2x + 4)\), you can use the distributive property (also known as the FOIL method for binomials). Here’s how it works step by step:

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

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

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

Answer 3

The product of the polynomials \((3x - 1)(2x + 4)\) can be expressed in the form \(Ax^2 + Bx + C\).

From the previous multiplication, we found:

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

So in the format \(Ax^2 + Bx + C\):

- \(A = 6\)
- \(B = 10\)
- \(C = -4\)

Therefore, you can fill in the blanks as follows:

- \( \text{blank} = 6 \) (for \(x^2\))
- \( \text{blank} = 10 \) (for \(x\))
- \( \text{blank} = -4 \) (for the constant term)

So, it would look like this:

**6x² + 10x - 4**