Multiply the polynomials (3x - 1) (2x + 4).

_x^2 + _x + _

1 answer

To multiply the polynomials \( (3x - 1)(2x + 4) \), we can use the distributive property, often referred to as the FOIL method for binomials, which stands for First, Outside, Inside, Last.

  1. First terms: \( 3x \cdot 2x = 6x^2 \)
  2. Outside terms: \( 3x \cdot 4 = 12x \)
  3. Inside terms: \( -1 \cdot 2x = -2x \)
  4. Last terms: \( -1 \cdot 4 = -4 \)

Now, combine all these results:

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

Combining the like terms (\( 12x - 2x \)) gives:

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

So the product of the polynomials \( (3x - 1)(2x + 4) \) is:

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

Filling in your blanks, we have:

\[ _x^2 + _x + _ \]

This translates to:

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

Thus, the completed expression is:

6, 10, -4