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.
8 answers
wondering the location of b.
Sorry! its g(x)=ax^3−x^2+bx−24
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
= (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
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
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
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.
lol! don't read my comment! i didn't see your new one before i posted mine!
how is ** - *** give - 24 ? shouldn't it be 4?
nvm got it! :) u did substitution right?
2 answers