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).
-
First, distribute \( 2x \): \[ 2x \cdot x = 2x^2 \] \[ 2x \cdot (-4) = -8x \]
-
Next, distribute \( 1 \): \[ 1 \cdot x = x \] \[ 1 \cdot (-4) = -4 \]
-
Now, combine all the terms: \[ 2x^2 - 8x + x - 4 \]
-
Combine the like terms \( -8x \) and \( x \): \[ -8x + x = -7x \]
Thus, the product of the polynomials is: \[ 2x^2 - 7x - 4 \]
1 answer