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