The given expression is: \(-2v^2 - 14v - 20\). This code...
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:
-
Factor out the greatest common factor (GCF) from all terms. [ GCF = -2 ] Factoring out (-2): [ -2(v^2 + 7v + 10) ]
-
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) ]
-
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.