Question

multiply the polynomials (3x-1)(2x+4)

__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 like terms (the \( x \) terms):
\( 12x - 2x = 10x \)

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

So, filling in the blanks:
- __x^2: **6**
- __x: **10**
- __: **-4**

The answer is:
\[
6x^2 + 10x - 4
\]