Asked by Sherry

The function g(x)=ax^3−x^2+x−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.
Answered by bobpursley
wondering the location of b.

Answered by Sherry
Sorry! its g(x)=ax^3−x^2+bx−24
Answered by Reiny
ax^3−x^2+bx−24
= (x-2)(x+4)(ax + c)

the ax^3 can only come from the multiplication of the first terms of each of the binomials,
(x)(x)(ax) = 3x^3 ----> a = 3
the -24 can only come from the multiplication of the last terms of each of the binomials,
(-2)(4)(c) = -24 ----> c = 3

thus: ax^3−x^2+bx−24
= (x-2)(x+4)(3x+3)

expand this, then match up the terms ending in x to find b
Answered by Reiny
forget the first part of my solution, I read it as
3x^3−x^2+bx−24

we know : f(x) = ax^3−x^2+bx−24

since x-2 is a factor, f(2) = 0
f(2) = 8a - 4 + 2b - 24 = 0
8a + 2b = 28
4a + b = 14 **

f(-4) = 0
-64a - 16 - 4b - 24 = 0
-64a - 4b = 40
16a+ b = -10 ***

subtract ** from ***
12a = -24
a = -2

in **
-8 + b = 14
b = 22


Answered by Sherry
but when i expand this i get 3x^3+9x^2-18x-24 and this doesn't work with the equation given as x^2 didn't have an coefficient and b was supposed to be positive.
Answered by Sherry
lol! don't read my comment! i didn't see your new one before i posted mine!
Answered by Sherry
how is ** - *** give - 24 ? shouldn't it be 4?
Answered by Sherry
nvm got it! :) u did substitution right?
There are no AI answers yet. The ability to request AI answers is coming soon!