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

Question

adrianluvvsyouu2 · Answer

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.

adrianluvvsyouu2 · Answer

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adrianluvvsyouu2 · Answer

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

surjithayer · Answer

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.

surjithayer · Answer

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