Please help me! For algebra 2 class. 45 points! Using the Fundamental Theorem of Algebra, complete the following exercises. Show your work.

Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.
Determine how many, what type, and find the roots for f(x) = x3 − 5x2 − 25x + 125.
The following graph shows a seventh-degree polynomial:
(see attachment)
Part 1: List the polynomial’s zeroes with possible multiplicities.
Part 2: Write a possible factored form of the seventh degree function.

Without plotting any points other than intercepts, draw a possible graph of the following polynomial:
f(x) = (x + 8)3 (x + 6)2 (x + 2)(x − 1)3 (x − 3)4 (x − 6).

1) There are four roots, with two real and two imaginary roots

The roots are x ±2, ±5·i

2) Therefore, there are 2 roots

The roots are real

The roots are x = -5 and x = 5

3) The possible factored form is therefore; (x + 5)²×(x + 1)×(x - 4)³×(x + 7)

4) Please see the attached graph of the function drawn with Microsoft Excel

Step-by-step explanation:

1) The given equations is as follows;

f(x) = x⁴ + 21·x² - 100

Let a = x², we have;

f(x) = a² + 21·a - 100

a = (-21 ± √(21² - 4 × 1 ×(-100))/(2 × 1)

a = -25 or 4

Therefore, x = √4 = ±2 or x = √(-25) = ±5·i

There are four roots, with two real and two imaginary roots

2) For f(x) = x³ - 5·x² - 25·x + 125

We have;

f(x) = x³ - 5·x² - 25·x + 125

From the equation, we see that x = 5 is a solution of the equation, therefore;

f(5) = 5³ - 5·5² - 25·5 + 125 = 0

Which gives, (x - 5) is a factor of the equation,

Dividing x³ - 5·x² - 25·x + 125 by (x - 5) gives;

x² - 25

(x³ - 5·x² - 25·x + 125)/(x - 5)

x³ - 5·x²

             - 25·x

               -25·x + 125

               0          +  0

Therefore, by long division, (x³ - 5·x² - 25·x + 125)/(x - 5) = x² - 25

(x - 5)×(x² - 25) = (x - 5) × (x - 5) × (x + 5)

Therefore, there are 2 roots

The roots are real

The roots are x = -5 and x = 5

3) From the polynomial zeros, we have x = -5, x = -1, x = 4, and x = 7

At x = -5 the polynomial touches the x-axis given two real roots with (x + 5)² being a factor

With the root at x = -1, a factor is (x - 1)

With the root at x = 4 which has the shape of a cubic function, we have a factor of (x - 4)³

For the root at x = 1, the factor is taken as (x + 7)

The possible factored form is therefore; (x + 5)²×(x + 1)×(x - 4)³×(x + 7)

4) The given function is therefore;

f(x) = (x + 8)³(x + 6)²(x + 2)(x - 1)³(x - 3)⁴(x - 6)

(x + 8)³(x + 6)²(x + 2)(x - 1)³(x - 3)⁴(x - 6)

Please see the attached graph of the function drawn with Microsoft Excel

answer: the answer is (b) amie should have multiplied

step-by-step explanation: given a sphere and a cylinder with same radius and height.

let, 'r' be the radius of the cylinder and sphere and 'h' be the height of the cylinder. according to the question,

r = h.

now, the volume of the sphere will be

and the volume of the cylinder will be

therefore, we have

thus, ammie should have multiplied the volume of the sphere

191 students play sports and ninety-seven 10th graders were surveyed.

step-by-step explanation: