Given the binomials (x-1), (x-3), (x+3), (x+5), which one is the factor of f (x) = x^3 + 6x^2 + 12x + 35?

The given polynomial is

f (x) = x³ + 6x² + 12x + 35

According to the Remainder Theorem, if x = a is a zero, then

f (a) = 0, and (x-a) is a factor.

Test (x-1):

f (1) = 1 + 6 + 12 + 35 = 54

Not a factor.

Test (x-3):

f (3) = 3³ + 6*3² + 12*3 + 35 = 152

Not a factor.

Test (x+3):

f (-3) = (-3) ³ + 6 * (-3) ² + 12 * (-3) + 35 = 26

Not a factor.

Test (x+5):

(-5) ³ + 6 * (-5) ² + 12 * (-5) + 35 = 0

It is a factor.

Answer: (x+5) is a factor.