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). Here's how it works step by step:
-
First: Multiply the first terms: \[ 2x \cdot x = 2x^2 \]
-
Outer: Multiply the outer terms: \[ 2x \cdot (-4) = -8x \]
-
Inner: Multiply the inner terms: \[ 1 \cdot x = 1x \quad \text{(or just } x\text{)} \]
-
Last: Multiply the last terms: \[ 1 \cdot (-4) = -4 \]
Now, combine all these results together: \[ 2x^2 - 8x + x - 4 \]
Combine like terms (\(-8x + x\)): \[ 2x^2 - 7x - 4 \]
Thus, the product of the polynomials \((2x + 1)(x - 4)\) is: \[ \boxed{2x^2 - 7x - 4} \]
3 answers