The given expression is: \(-2v^2 - 14v - 20\). This code...

February 4, 2025 at 06:24 PM

Factor Completely minus, 2, v, squared, minus, 14, v, minus, 20 −2v 2 −14v−20 Answer Attempt 1 out of 3

The given expression is: (-2v^2 - 14v - 20).

This code or expression represents a quadratic equation, and "Factor Completely" indicates the process of factoring the polynomial into smaller terms.

Process:

The expression can be factored as follows:

  1. Factor out the greatest common factor (GCF) from all terms. [ GCF = -2 ] Factoring out (-2): [ -2(v^2 + 7v + 10) ]

  2. Factor the quadratic (v^2 + 7v + 10): To factor (v^2 + 7v + 10), find two numbers that multiply to (10) (the constant term) and add to (7) (the coefficient of (v)):

    • These numbers are (5) and (2).

    Therefore: [ v^2 + 7v + 10 = (v + 5)(v + 2) ]

  3. Rewrite the fully factored form: [ -2v^2 - 14v - 20 = -2(v + 5)(v + 2) ]

Final Answer:

The code or expression factors the quadratic (-2v^2 - 14v - 20) completely into: [ -2(v + 5)(v + 2) ]

This is the completely factored form of the given polynomial.

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