The Rational Roots Theorem

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

A,B,E

Which of the numbers below are some potential roots of p(x) = x3 + 6x2 − 7x − 60 according to the rational root theorem?

A,C,D,E

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

A,C,E

Use synthetic division to test one potential root. Enter the numbers that complete the division problem. −5 1 6 −7 −60a −c −601 b −d −60

A=-5 B=1 C=-5 D=-12

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

B

Select all of the following that are potential roots of p(x) = x4 − 9x2 − 4x + 12?

B,CF,G,H

An open box is to be made from a rectangular piece of cardboard that measures 6 in. by 3 in., by cutting out squares of the same size from each corner and bending up the sides. Is it possible to cut the squares so that the volume of the box is40 in.3? Find all real solutions of this equation to answer the question.(6 - 2x)(3 - 2x)x = 40

D

Evaluate the function for the given values to determine if the value is a root.

P(-2)= 0 P(2)=-16 -2

Determine whether the rational root theorem provides a complete list of all roots for the following polynomial functions.

yes no, this polynomial has complex roots no, this polynomial has irrational root

Write the polynomial in factored form.p(x) = (x + 5)(x −

3 4

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

The root of a number x is another number, which when multiplied by itself a given number of times, equals x. For example the second root of 9 is 3, because 3x3 = 9. The second root is usually called the square root. The third root is susually called the cube root See Root (of a number).