To factor B(x)=2x^3-x^2-27x+36( x-3÷2) into linear factors of 2(x - 3/2)(x + 4)(x - 3).
Factor out the common factor of 2:
B(x) = 2(x^3 - (1/2)x^2 - (27/2)x + 18)
Using synthetic division to test possible roots, x = 3/2 is a root.
3/2 | 2 -1/2 -27/2 18
| 3 1/2 -27/2
|-------------------
2 2-1/2 -26/2 0
We write the polynomial as a product of linear factors:
B(x) = 2(x - 3/2)(x^2 + (5/2)x - 12)
Further factor the quadratic factor based on:
(x + 4)(x - 3) = x^2 + x - 12
Therefore:
B(x) = 2(x - 3/2)(x + 4)(x - 3)
Thus, B(x) can be factored into the linear factors of 2(x - 3/2)(x + 4)(x - 3).