Factorize 2x^4-7x^3-13x^2+63x-45 using factor theorem.

Find the possible rational roots and use synthetic division to find the first zero.
I chose x=1 (which represents the factor "x-1")

1║2  -7  -13    63  -45
  ║     2    -5  -18    45
    2  -5  -18    45    0
(x-1) is a factor, (2x³ - 5x² - 18x + 45) is the other factor.

Use synthetic division on the decomposed polynomial to find the next zero.
I chose x = 3 (which represents the factor "x-3")

3║2  -5  -18    45 
  ║     6     3   -45   
    2   1  -15     0   

Using synthetic division, we discovered that (x-1), (x-3), & (2x² + x -15) are factors.  Take the new decomposed polynomial (2x² + x -15) and find the last two factors using any method.

Final (x-1)(x-3)(x+3)(2x-5)

Don’t worry about it