The Rational Roots Theorem Answers

Which of the number(s) below are potential roots of the function?p(x) = x4 + 22x2 – 16x – 12

Which of the number(s) below are potential roots of the function?q(x) = 6x3 + 19x2 – 15x – 28

Using the section of the graph shown, which of these potential roots of the function should you test first?f(x) = 2x3 – 9x2 – 6x + 40

According to the rational root theorem, the numbers below are some of the potential roots of f(x) = 10x3 + 29x2 – 66x + 27. Select all that are actual roots.

0±2±4 ±9±3±6 ±12

Evaluate the function for the given values to determine if the value is a root. p(−2) = p(2) = The value is a root of p(x).

–16✔ –202

f(x) = 4x2 − 25 g(x) = 4x2 + 25 h(x) = 3x2 − 25

✔ No, this polynomial has complex roots.No, this polynomial has irrational roots.No, this polynomial has irrational and complex roots.Yes.

No, this polynomial has complex roots.✔ No, this polynomial has irrational roots.No, this polynomial has irrational and complex roots.Yes.

–10 –7–531524

Use synthetic division to test one potential root. Enter the numbers that complete the division problem. −5 1 6 −7 −60 a −c −60 1 b −d −60 a = ⇒ -5 b = ⇒ 1 c = ⇒ -5 d = ⇒ -12

⇒ 3

Find all real solutions of this equation to answer the question.(6 – 2x)(3 – 2x)x = 40

Yuri thinks that is a root of the following function.q(x) = 6x3 + 19x2 – 15x – 28Explain to Yuri why cannot be a root.