Question

50 points! A polynomial has been factored below, but some constants are missing. 2x^3 - 8x^2 - 24x = ax (x+b)(x+c) What are the missing values of a, b, and c?

Answer 1

Answer:

In the given expression $2x^3 - 8x^2 - 24x = ax (x+b)(x+c)$,  

a = 2 , b = - 6 and c  = 4

Step-by-step explanation:

Here, the given polynomial is given as: $2x^3 - 8x^2 - 24x = ax (x+b)(x+c)$

Now, to find the missing values of the constants a , b and c factorize the given polynomial.

We have:

$2x^3 - 8x^2 - 24x = 2x( x^2 - 4x -12) \\= 2x(x^2 - 6x + 4x -12) \\= 2x(( x-6)+ 4(x-6)) = 2x (x-6)(x+4)\\\implies 2x^3 - 8x^2 - 24x = 2x (x-6)(x+4)$

or,

2 x (x - 6)(x + 4) = ax (x + b)(x + c)

Comparing the two given expressions, we get

2 x= a x

x + (- 6)  = x + b

x + c  = x + 4

⇒   a =2, b = - 6 and c  = 4

Hence, in the given expression $2x^3 - 8x^2 - 24x = ax (x+b)(x+c)$,  a =2, b = - 6 and c  = 4.