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Find the product of the polynomials (2x+1)(x−4)

.(2 points)
__x^2+____x+___

1 answer

To find the product of the polynomials \( (2x + 1)(x - 4) \), we will use the distributive property (also known as the FOIL method for binomials).

  1. Multiply the first terms: \( 2x \cdot x = 2x^2 \)
  2. Multiply the outer terms: \( 2x \cdot (-4) = -8x \)
  3. Multiply the inner terms: \( 1 \cdot x = 1x \) (or just \( x \))
  4. Multiply the last terms: \( 1 \cdot (-4) = -4 \)

Now, we combine all these results: \[ 2x^2 - 8x + x - 4 \]

Combine the like terms \( -8x + x = -7x \):

Thus, the final polynomial is: \[ 2x^2 - 7x - 4 \]

So, filling in the blanks: \[ __x^2 + __x + __ \] becomes \[ 2x^2 + (-7)x + (-4) \]

Therefore, the answer is: \[ 2x^2 - 7x - 4 \]