The given polynomial is : x³ - 5x² - 18x + 72
To factorize the polynomial
In the given option the factors are (x-3), (x+4), (x - 6) (x -2), (x+2)
Apply hit and trial method
Substitute x = 3 if the polynomial satisfy then the (x - 3) is the factor
x³ - 5x² - 18x + 72
3³ -5 3² - 18 ( 3) + 72
27 - 45 - 54 + 72
0
Thus x = 3 satisfy the polynomial
hence ( x - 3) is the factor of the polynomial
Now for the other factors : Divide the polynomial x³ - 5x² - 18x + 72 by ( x - 3)
Thus, on x³ - 5x² - 18x + 72 by ( x - 3) = x² - 2x - 24
Factorize : x² - 2x - 24
x² - 2x - 24 = 0
x² - 6x + 4x - 24 = 0
x(x - 6) + 4 (x - 6) = 0
(x + 4)(x - 6) = 0
So the factors are (x + 4) (x - 6)(x - 3)
Answer : A) (x + 4) (x - 6)(x - 3)