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 Answer: (x-1) (x-3) (x+3) (2x-5)