Answer:
Then the four zeros of the given polynomial are {-1, -5, -1, +1}
Step-by-step explanation:
First, make an educated guess regarding the first zero of this polynomial. Since the constant term is 5, likely zeros are -1, 1, -5 and 5. Let's check out the possible zero -1, using synthetic div.:
-1 / 1 6 6 6 5
-1 -5 -1 -5
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1 5 1 5 0 These are the coefficients of the quotient.
Because the remainder is zero, we know that -1 is a zero of the given polynomial.
Next, let's determine whether -5 is a zereo of the above quotient:
------------------------------
-5 / 1 5 1 5
-5 0 -5
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1 0 1 0 Because the remainder is zero, -5 is a zero.
Here the quotient is 1x^2 - 1^2, which factors into (x+1)(x-1)
Setting this result = to 0, we get x = -1 and x = + 1.
Then the four zeros of the given polynomial are {-1, -5, -1, +1}
