Question

Which of the following is linear factors? a factor of x ^ 3 - 5x ^ 2 - 2x + 24 given that x - 3 is one of the linear factors
I think it’s either x-2 or x+4

Answer 1

You can use polynomial division to find other factors, knowing that (x-3) is one of the roots, and the function is a cubic, there should be another 2 factors.

Answer 2

It's hard to explain polynomial long division without a video, so you should be able to find something on khan academy that has a good explanation

Answer 3

put x-3=0
x=3
find the value of \[x^3-5x^2-2x-24\] at x=3
\[3^3-5(3)^2-2(3)-24=27-45-6+24=51-51=0\]
so x-3 is a linear factor.
similarly put x-2=0,x=2 in the given equation.
and x+4=0,x=-4
where the value comes out to be equal to zero.
That is a linear factor.

Answer 4

or by synthetic division
3 |1 -5 -2 +24
| 1 3 -6 -24
_________________
1 -2 -8 |0
\[x^2-2x-8=0\]
\[x^2-4x+2x-8=0\]
x(x-4)+2(x-4)=0
(x-4)(x+2)=0
so other linear factor is x+2,x-4