Identify two expressions that will be equivalent to 2x2−8x−10

Question

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 #
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Answer 1

To find expressions that are equivalent to \( 2x^2 - 8x - 10 \) when distributed, we can simplify each option.

1. Option #1: \( 2x(x - 4x - 5) \)

   Simplifying: \[ 2x(x - 4x - 5) = 2x(-3x - 5) = -6x^2 - 10x \] This does not match the original expression.

2. Option #2: \( (2x + 2)(x - 5) \)

   Simplifying: \[ (2x + 2)(x - 5) = 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \] This matches the original expression.

3. Option #3: \( 2x(x - 5) + 2(x - 5) \)

   Simplifying: \[ 2x(x - 5) + 2(x - 5) = (2x + 2)(x - 5) = 2x^2 - 8x - 10 \] This also matches the original expression.

4. Option #4: \( (x - 5)(x - 3) \)

   Simplifying: \[ (x - 5)(x - 3) = x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \] This does not match the original expression.

5. Option #5: \( -6x - 10 \)

   This expression is not quadratic and does not match the original expression.

Therefore, the options that match \( 2x^2 - 8x - 10 \) are Option #2 and Option #3.

So, the answer is:

Option #2 and Option #3.