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

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

  1. First, distribute \( 2x \): \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-4) = -8x \]

  2. Next, distribute \( 1 \): \[ 1 \cdot x = x \] \[ 1 \cdot (-4) = -4 \]

  3. Now, combine all the terms: \[ 2x^2 - 8x + x - 4 \]

  4. Combine the like terms \( -8x \) and \( x \): \[ -8x + x = -7x \]

Thus, the product of the polynomials is: \[ 2x^2 - 7x - 4 \]