The roots of any equation, always satisfies that equation.
Values of , a = - 2 and b = 22
Other factor of given function is (x - 3/2)
The given function [tex]f(x) = ax^3 -x^2 + bx -24[/tex]
Since, (x - 2) and (x + 4) are factors of given function
Therefore, x = 2 and x = -4 satisfies the given function.
[tex]f(2)=8a-4+2b-24=0\\8a+2b=28\\\\f(-4)=-64a-16-4b-24=0\\-64a-4b=40\\-16a-b=10[/tex]
Now , solving above two equation by elimination method
We get, a = -2 and b = 22
So, [tex]f(x) = -2x^3 -x^2 + 22x -24[/tex]
To find other factors , we divide above function by multiplication of (x - 2)(x+4).
So we get other factors, (x - 3/2)
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