What is the expression in factored form?
2x^2+16x+24
Is it (x-2)*(x-6) or 2(x-2)*(x-6)?
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 )
Thank you!
To find the factored form of the expression 2x^2 + 16x + 24, we need to factor out the common factor, if any, and then factorize the remaining quadratic trinomial.
First, let's look for a common factor, which is 2 in this case. We can factor out the 2 from each term:
2(x^2 + 8x + 12)
Next, we need to factorize the quadratic trinomial x^2 + 8x + 12. To do this, we look for two numbers that multiply to give us 12 and add up to give us 8. In this case, those numbers are 6 and 2:
(x + 6)(x + 2)
So, the factored form of the expression 2x^2 + 16x + 24 is 2(x + 6)(x + 2).
Therefore, the correct answer is 2(x + 6)(x + 2), not (x - 2)(x - 6).