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.
