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

.(2 points)

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: \[ 1 \cdot x = x \]

  4. Multiply the last terms: \[ 1 \cdot (-4) = -4 \]

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

Next, combine the like terms \(-8x\) and \(x\): \[ 2x^2 - 7x - 4 \]

Thus, the product of the polynomials \( (2x + 1)(x - 4) \) is: \[ \boxed{2x^2 - 7x - 4} \]