Use the following to answer questions :
p(x) = x 4 - 5x 3 + 5x 2 + 5x - 6
-Use the information gathered, testing for 1 and -1, synthetic division, and the factor theorem to factor p completely.
A) p(x) = (x + 1)(x - 1)(x + 2)(x + 3)
B) p(x) = (x + 1)(x - 1)(x - 2)(x + 3)
C) p(x) = (x + 1)(x - 1)(x + 2)(x - 3)
D) p(x) = (x + 1)(x - 1)(x - 2)(x - 3)

Question

Quizplus · Accepted Answer

Using synthetic division with 1 and -1 shows that both are roots of the polynomial, meaning it is divisible by (x-1) and (x+1). Then, using the factor theorem, we can see that (x+2) and (x+3) are also roots of the polynomial, making the factorization (x+1)(x-1)(x-2)(x-3). Therefore, the best choice is D.

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