Answer:
In the given expression [tex]2x^3 - 8x^2 - 24x = ax (x+b)(x+c)[/tex],
a = 2 , b = - 6 and c = 4
Step-by-step explanation:
Here, the given polynomial is given as: [tex]2x^3 - 8x^2 - 24x = ax (x+b)(x+c)[/tex]
Now, to find the missing values of the constants a , b and c factorize the given polynomial.
We have:
[tex]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)[/tex]
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 [tex]2x^3 - 8x^2 - 24x = ax (x+b)(x+c)[/tex], a =2, b = - 6 and c = 4.
