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
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.
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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
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.
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
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