The function f(x) = ax^3 -x^2 + bx -24 has three factors. Two of these factors are x-2 and x+4. Determine the values of a and b, then determine the other factor. (My Nelson Advanced Functions Grade 12 book chapter 3)

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mathanswer mathanswer · Answer 1 · 2017-10-01T18:20:17+02:00

Answer is below........

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ibiscollingwood ibiscollingwood · Answer 2 · 2021-10-10T14:08:53+02:00

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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