Question

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

Answer 1

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 to do it step by step:

1. Distribute \( 2x \) to both terms in the second polynomial:
\[
2x \cdot x = 2x^2
\]
\[
2x \cdot (-4) = -8x
\]

2. Distribute \( 1 \) to both terms in the second polynomial:
\[
1 \cdot x = x
\]
\[
1 \cdot (-4) = -4
\]

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

4. Combine like terms:
\[
2x^2 + (-8x + x) - 4 = 2x^2 - 7x - 4
\]

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