To Add Polynomials

Alice and Bob are playing with numbers. Alice writes down the equation 
(3- 2x + 2x²) and Bob writes down (4x -5 +3x²). Find the difference between Alice's and Bob's equations.

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

John is managing his budget for the month. He records his income as (3- 2x + 2x²) dollars and his monthly bills as (4x -5 +3x²) dollars. Calculate the difference between his income and bills. 

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Imagine you're an agricultural scientist named Dr. Green working on a project that involves calculating the growth of two different types of crops over time. The growth of Wheat crop is represented by the equation 7x² - 3x, and the growth of Corn crop is represented by 5x² + x + 3. You need to combine these equations to predict the total growth of these crops. What equation represents the total growth?

• 12x² - 2x + 3

• 2x² + 4x + 3

• 12x⁴ + 2x² + 3

• 2x² - 4x - 3

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

Add the following polynomials: 
(6x + 4x⁴ - 3x²) + (7x⁴ + 5x² + 8x)

• 11x⁴  + 2x² + 14x

• 16x⁴  + x² + 14x

• 11x⁴  + x² + 14x

• 11x⁴  + 2x² + 10x

Add the following polynomials:
 (5x + 2) + (4x + 5)

• 9x -7

• -9x-11

• 9x+7

• x+7

Add the following polynomials:
(6n² - 7n⁴+8) +  (6 + 8n + 4n⁴)

• -3n⁴+ 6n²+8n+14

• -n⁴-2n²+8n+7

• -n⁴ + 6n²+8n+7

• -3n⁴+ 6n²+8n+7

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

• 3x³ + 5

• 3x³ + 8x + 5

• 3x² + 5

• 7x³ + 8x + 5

Find the product:
-3x²( 7x² - x + 4)

• -21x⁴ + 3x³ -12x²

• 7x² - x + 4 (-3x²)

• 21x⁴ + 3x³ + 12x²

• -12x² + 3x³ -21x⁴