Question

5 of 85 of 8 Items


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

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

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

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

Fill in the blanks:
- First blank (for \( x^2 \)): **6**
- Second blank (for \( x \)): **10**
- Third blank (constant term): **−4**

Thus, the answer is:
\[
6x^2 + 10x - 4
\]