Question

Use the rational zero test to find all the rational zeros of f(x). 10) f(x) = 5x4 + 7x3 - 18x2 - 28x - 8 A) Zeros: -1, 2/5, 2, -2 C) Zeros: 1, -2/5, 2, -2 B) Zeros: 1, 2/5, 2, -2 D) Zeros: -1, -2/5, 2, -2 11) f(x) = 4x³ + 13x2 - 37x - 10 A) Zeros: -5, 2, -1/4 C) Zeros: 5, -2, 1/4 B) Zeros: 5, -2, 1 D) Zeros: -5, 2, -1

Answer 1

10) To use the rational zero test, we need to find all the possible rational zeros of the polynomial. The possible rational zeros are all the factors of the constant term (-8 in this case) divided by all the factors of the leading coefficient (5 in this case).

Possible rational zeros: ±1, ±2, ±4, ±8 ÷ 1, ±5 ÷ 5

Simplifying: ±1, ±2/5, ±2, ±4/5, ±8/5

Now we can test each of these values to see which ones are actually zeros of the polynomial. We can use synthetic division or long division to test each value, or we can use a graphing calculator. Testing each value, we find that the zeros are -1, 2/5, 2, and -2.

Therefore, the answer is (A) Zeros: -1, 2/5, 2, -2.

11) Using the same process as in problem 10, we find the possible rational zeros to be: ±1, ±2, ±5, ±10 ÷ 1, ±4 ÷ 4

Simplifying: ±1, ±2, ±5, ±10 ÷ 4

Testing each value, we find that the zeros are -5, 2, and -1/4.

Therefore, the answer is (A) Zeros: -5, 2, -1/4.