Question

What is the expression in factored form?

2x^2+16x+24

Is it (x-2)*(x-6) or 2(x-2)*(x-6)?

Answer 1

2 x² + 16 x + 24 = 2 ( x² + 8 x + 12 )

Now solve:

x² + 8 x + 12 = 0

The solutions are:

x1 = - 2 , x2 = - 6

Each quadratic equation can be written in the form:

a x² + b x + c = a ( x - x1 ) ( x - x2 )

In this case:

x² + 8 x + 12 = 1 ∙ [ x - ( - 2 ) ] [ x - ( - 6 ) ] = ( x + 2 ) ( x + 6 )

So:

2 x² + 16 x + 24 = 2 ( x² + 8 x + 12 ) = 2 ( x + 2 ) ( x + 6 )

Answer 2

Thank you!