Question

use the distributive property to rewrite the polynomial (2x+1)(x-4)

Answer 1

2 is right but the other ones are not

Answer 2

To use the distributive property to rewrite the polynomial \((2x + 1)(x - 4)\), we will distribute each term in the first polynomial by each term in the second polynomial.

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

2. Distributing \(1\) to both terms in \((x - 4)\):
\[
1 \cdot x = x
\]
\[
1 \cdot (-4) = -4
\]

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

Next, combine like terms \(-8x + x\):
\[
2x^2 - 7x - 4
\]

So, the polynomial \((2x + 1)(x - 4)\) rewritten is:
\[
\boxed{2x^2 - 7x - 4}
\]

Answer 3

Let's redo the calculation for \((2x + 1)(x - 4)\) using the distributive property step by step.

1. **Distribute \(2x\)** over \((x - 4)\):
- \(2x \cdot x = 2x^2\)
- \(2x \cdot (-4) = -8x\)

2. **Distribute \(1\)** over \((x - 4)\):
- \(1 \cdot x = x\)
- \(1 \cdot (-4) = -4\)

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

Next, combine the like terms \(-8x + x\):
\[
2x^2 - 7x - 4
\]

The final rewritten polynomial is:
\[
\boxed{2x^2 - 7x - 4}
\]

Please let me know if there's something specific you believe is incorrect or if there's further clarification needed!