Finding all possible rational zeros using the rational zeros theorem: Problem type 1

Question

Use the rational zeros theorem to list all possible rational zeros of the following.

g(x) = −x³ + 4x² − 5x - 7

Be sure that no value in your list appears more than once.

Answer 1

7/1, -7/1, 1/1,-1/1

= 7, -7, 1 or -1

take integer factors of the constant term as numerators

over integer factors of the leading term as denominators

eliminate duplicates such as -7/1 = 7/-1, -1/1= 1/-1, 7/1=-7/-1, 1/1 = -1/-1