Answer:
In the given expression
,
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)](https://tex.z-dn.net/?f=2x%5E3%20-%208x%5E2%20-%2024x%20%3D%20ax%20%28x%2Bb%29%28x%2Bc%29)
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)](https://tex.z-dn.net/?f=2x%5E3%20-%208x%5E2%20-%2024x%20%20%3D%202x%28%20x%5E2%20-%204x%20-12%29%20%5C%5C%3D%202x%28x%5E2%20-%206x%20%2B%204x%20-12%29%20%20%5C%5C%3D%202x%28%28%20x-6%29%2B%204%28x-6%29%29%20%20%3D%202x%20%28x-6%29%28x%2B4%29%5C%5C%5Cimplies%202x%5E3%20-%208x%5E2%20-%2024x%20%3D%202x%20%28x-6%29%28x%2B4%29)
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
, a =2, b = - 6 and c = 4.