Question

Factorise x 3 - 3 x2 - 10 X + 24

Answer 1

The roots must be factors of 24. Because the numbers -3 and -10 are relatively small, the most probable roots woild be -4, -3, -2, -1, 1, 2, 3, or 4 
Use synthetic division and find that the smallest root is -3, So you can now rewrite it as 
(x + 3)(x^2 - 6x + 8) 
The second factor can be factored as (x - 2)(x - 4) 
So the factored form is (x + 3)(x - 2)(x - 4) 
and the roots are -3, 2, and 4

Answer 2

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