Question

Solve the quadratic equation and Factor v*2+5v+6=0

Answer 1

v = -2 or v= -3 are possible solutions

Explanation:

In order to factor out this polynomial, we need to find two numerical factors whose product is "6" (the constant term of the polynomial), and whose combining renders "5" (the coefficient of the middle term).

We notice that "3" and 2" are such factors since 3*2 = 6, and 3+ 2 = 5. So we use them to split the middle term of the polynomial, and then use factoring by grouping:

`v^2+5v+6=0\\v^2+3v+2v+6=0\\v(v+3)+2v+6=0\\v(v+3)+2(v+3)=0\\(v+3)(v+2)=0`

So we have now the binomial factors that render the polynomial. For the polynomial to render zero, either factor must give zero. That is:

`(v+3)=0\\v=-3`

or

`(v+2)=0\\v=-2`

Therefore, either -2 or -3 are possible solutions to the equation.