Question

Find the polynomials (2x+1) (x-4)

Answer 1

To find the polynomial resulting from multiplying \( (2x + 1)(x - 4) \), we can 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:
\( 1 \cdot x = 1x \) (or just \( x \))

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

Now we combine all these results together:
\[
2x^2 - 8x + x - 4
\]

Next, we combine like terms:
\[
2x^2 - 7x - 4
\]

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