Question

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

2x^2+_x+_

Answer 1

To find the product of the polynomials \( (2x + 1)(x - 4) \), we will apply 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 results:
\[
2x^2 - 8x + x - 4
\]
Combine the like terms (-8x and x):
\[
2x^2 - 7x - 4
\]

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

Thus, the coefficients for your question will be:
- For the coefficient of \( x \): \(-7\)
- For the constant term: \(-4\)

Final answer:
\[
2x^2 - 7x - 4
\]