Ask a New Question
Menu

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
Option # __ and Option # __

1 answer

To find the equivalent expressions of \(2x^2 - 8x - 10\), we will distribute each of the options provided and see which ones give us that polynomial.

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

    • This seems incorrect because \(4x\) should not be subtracted within the parentheses. However, if we clarify it, let's assume it meant \(2x(x - 4) - 5\) which is incorrect.

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

    • Distributing gives: \[ 2x \cdot x + 2 \cdot x - 2x \cdot 5 - 2 \cdot 5 = 2x^2 + 2x - 10x - 10 = 2x^2 - 8x - 10 \]
    • This matches.

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

    • We can factor this: \[ (2x + 2)(x - 5) = 2x^2 - 8x - 10 \]
    • This also matches (same as Option #2).

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

    • Distributing gives: \[ x \cdot x - 3 \cdot x - 5 \cdot x + 15 = x^2 - 8x + 15 \]
    • This does not match.

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

    • This does not match the polynomial \(2x^2 - 8x - 10\), as it is a linear expression.

After evaluating the options, the two that are equivalent to \(2x^2 - 8x - 10\) are Option #2 and Option #3.

Since we want to enter the option with the lesser number first, the answer is:

Option #3 and Option #2