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 expressions are equivalent to \( 2x^2 - 8x - 10 \) when distributed, let's simplify each option.

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

   • Simplifying: \[ 2x(-3x - 5) = -6x^2 - 10x \] (Not equivalent)

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

   • Distributing: \[ 2x(x) + 2(x) - 10x - 10 = 2x^2 - 8x - 10 \] (This is equivalent)

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

   • Distributing: \[ 2x^2 - 10x + 2x - 10 = 2x^2 - 8x - 10 \] (This is equivalent)

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

   • Distributing: \[ x^2 - 3x - 5x + 15 = x^2 - 8x + 15 \] (Not equivalent)

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

   • Not matching the degree of the polynomial.

From our analysis, the two equivalent expressions are:

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

Thus, the answer is:

Option #2 and Option #3