Answer :

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)




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