Question

Identify two expressions that will be equivalent to 2x2−8x−10 when distributed. Enter the option with the lesser number first.

Option #1: 2x(x−4x−5)

Option #2: (2x+2)(x−5)

Option #3: 2x(x−5)+2(x−5)

Option #4: (x−5)(x−3)

Option #5: −6x−10

(1 point)
Option # and Option #

Answer 1

To determine which options are equivalent to the expression \(2x^2 - 8x - 10\) when distributed, we need to simplify each option and see if it matches the original expression.

1. **Option #1: \(2x(x - 4x - 5)\)**
This expression has a mistake in parentheses, it should be \(2x(x - 4)\) since it's not a standard syntax. Let's consider it as \(2x(x - 4 - 5)\) which gives \(2x(x - 9)\).
Distributed:
\[ 2x \cdot x - 18x = 2x^2 - 18x \]
This does not match \(2x^2 - 8x - 10\).

2. **Option #2: \((2x + 2)(x - 5)\)**
Distribution gives:
\[ 2x \cdot x + 2 \cdot x - 10x - 10 = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \]
This matches!

3. **Option #3: \(2x(x - 5) + 2(x - 5)\)**
This can be factored as:
\[ (2x + 2)(x - 5) \]
We already determined this as Option #2.

4. **Option #4: \((x - 5)(x - 3)\)**
Distributing yields:
\[ x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \]
This does not match \(2x^2 - 8x - 10\).

5. **Option #5: \(-6x - 10\)**
This is clearly not equivalent to \(2x^2 - 8x - 10\).

Thus, the two equivalent options from the given list are Option #2 and Option #3.

The final answer would be:
**Option #2 and Option #3**.