Add, Subtract Polynomials

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

(4x³-5x²+3x)+(-2x³-x²+6x)

• 2x³-6x²-9x

• 2x³+6x²+9x

• -2x³-6x²+9x

• 2x³-6x²+9x

Add or Subtract to Simplify:
 (4x - 2x³) + (5x³ - 4x + 5)

• 3x³ + 5

• 3x³ + 8x + 5

• 3x² + 5

• 7x³ + 8x + 5

Find the sum.
(3y² + y³ - 5) + (4y² -4y + 2y³ + 8)

• 3y³ + 7y² - 4y + 3

• 4y² + 3y³ - y + 3

• -y⁴ + 2y³ -y - 4

• 4y³ + 3y² -3y + 1

Add or Subtract to Simplify:
(4x²+ x) - (x²+ 2x)

• 3x² - x

• 4x² + 2x

• 3x² + 3x

• 3x² + 2x

(7x² - 3x) + (5x² + x + 3)

• 12x² - 2x + 3

• 2x² + 4x + 3

• 12x⁴ + 2x² + 3

• 2x² - 4x - 3

Add or Subtract to Simplify:
(x⁵ + x³) - (6x - x³ + 6x⁵)

• -5x⁵ + 2x³ - 6x

• 7x⁵ - 6x

• -5x³ + 2x² - 6x

• -5x⁵ - 6x

Simplify (5x⁴ - 4x³ - 2x² + x - 19) - (x⁴ + 5x³ + 8x² + x + 5)

• 4x⁴ - 9x³ - 10x² - 24

• 4x⁴ - 9x³ - 10x² - 2x - 24

• 4x⁴ - 9x³ - 10x² + 2x - 24

• -4x⁴ - 9x³ - 10x² - 24