Question

Multiply the polynomials (3x – 1)(2x + 4)

_x^2 + _x + _

Fill the blanks

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, we combine all these results:

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

Combining like terms gives:

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

So the completed polynomial is:

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

Filling in the blanks for your question:

_x^2 + _x + _

is:

6 (for the x^2 coefficient), 10 (for the x coefficient), and -4 (the constant term).

Thus, the answer is:

**6, 10, -4**