The Rational Roots Theorem Assignment

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 -5 -2 1 8

-2

Yuri thinks that is a root of the following function. q(x) = 6x^3 + 19x^2 - 15x - 28 Explain to Yuri why cannot be a root.

3/4 cannot be a factor because none of the factors of 6 which is the q value are four. The factors of the p value, in this case 28, must go over one of the q values

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 is 40 in.3? Find all real solutions of this equation to answer the question.(6 - 2x)(3 - 2x)x = 40 -Yes. Because is a root, you can cut squares with sides of in. to make the box -No. This equation has no real solutions. -No. The only real solution is x = 4. It is not possible to cut squares of this size.

C.

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

a: 3 b: 4

Which of the number(s) below are potential roots of the function?q(x) = 6x3 + 19x2 - 15x - 28 ±2/3 ±7/2 ±1/7 ±6 ±14 ±3/5

A. B. & E.

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. -9/2 -9/10 3/5 1 3

A. C. & D.

Which of the number(s) below are potential roots of the function?p(x) = x4 + 22x2 - 16x - 12 ±6 ± 1/3 ±1 ±11/2 ±3 ±8

A. C. & E.

Which of the numbers below are some potential roots of p(x) = x3 + 6x2 − 7x − 60 according to the rational root theorem? -10 -7 -5 3 15 24

A. C. D. & E.

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).

A: 0 B: -16 C: -2

Determine whether the rational root theorem provides a complete list of all roots for the following polynomial functions. f(x) = 4x^2 − 25_______________________________ g(x) = 4x^2 + 25______________________________ h(x) = 3x2 − 25________________________________

A: yes B: No, this polynomial has complex roots C: No, this polynomial has irrational roots

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

Select all of the following that are potential roots of p(x) = x4 − 9x2 − 4x + 12? 0 ±2 ±4 ±9 1/2 ±3 ±6 ±12

B. C. F. G. & H.