Creating Polynomial Equations

Sarah is planning to install a fence around her rectangular vegetable garden. If the length of the garden is represented by 'x+2' and the width by 'x-3', what is the total length of the fence needed to enclose the garden?

• x²+8x-5

• 2x²+16x-10

• 2x²+10x-8

• 6x-2

Lisa is calculating the total expenses for her bakery's renovation project. She initially estimated the expenses as (4n⁴ - 8n + 4) dollars. However, after a detailed review, she found an overestimation of (8n² + 4n⁴ + 1) dollars in her calculation. What is the corrected total expenses?

• -8n² - 8n + 3 

• -7n² - 8n + 3 

• -6n² - 8n + 3

• -7n² - 4n + 3

At Lucy's Cafe, Lucy is working on the financials for the month. She applies the formula:
(6c³ + 6 - c⁴) - (8c³ - 6c⁴ + 2) to calculate her monthly expenses and profits, where c represents the number of coffee batches brewed. Simplify the expression to find the formula for her monthly financial calculation.

• 4c⁴ - 2c³ + 7

• 5c⁴ - 2c³ + 4

• c⁴ - 2c³ + 7

• 5c⁴ - 2c³ + 7

Sarah is planning a small party and is calculating the total cost of decorations and snacks she bought. She spent on decorations
 (5x + 2) dollars and on snacks
 (4x + 5) dollars. Combine like terms to find the total cost.

• 9x -7

• -9x-11

• 9x+7

• x+7

Two engineers are working on a project to optimize a network's data flow. Engineer A improves the network's efficiency with a polynomial improvement of (3x³ + 3x² – 4x + 5), while Engineer B finds another optimization represented by (x³ – 2x² + x – 4). What is the combined improvement to the network's efficiency when both optimizations are applied?

• 4x³ + 1x² – 3x + 1

• 2x³ + 1x² - 5x + 9

• 6x³ + 1x - 1x² - 3

• 3x⁵ +1x - 1x⁵ - 3x

Solve by factoring:
x² - 9x = 0

• 9

• 0, 9

• -9, 0

• -9

How many zeros does the polynomial function
y = 3x⁴ + 4x - 8 have?

• 1

• 2

• 3

• 4

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

Write the polynonmial from the following zeros.

 x = -2, 1, 4

If you know 3 and 2i are roots of a polynomial function, state the polynomial factors.

• (x + 3) , (x + 2i)

• (x - 3), (x -2i), (x + 2i)

• (x - 3), (x + 3), (x - 2i), (x + 2i)

• (x -3 - 2i), (x + 3 - 2i)