Add Subtract Polynomial

A mathematician named Dr. Euler is working on polynomial expressions for a new mathematical model and encounters the following problem while simplifying an equation:
(p³ - 6p⁴ + 1) - (8p⁴ - 8p³ + 7)

• -14p⁴ + 9p³ - 6

• -14p⁴ + 9p³ + 6

• -14p⁴ + 9p³ - 1

• -15p⁴ + 9p³ + 6

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

John and Emily are planning to prepare two types of cookies for a local charity event. The first cookie recipe requires ingredients costing (2x² + 5x - 7) dollars, and the second cookie recipe requires ingredients costing (3 - 4x² + 6x) dollars. How much will the ingredients for both cookie types cost in total?

• 2x² + 3x +1

• -2x² - 11x -4

• 2x² + 5x -7

• -2x² + 11x -4

Alice is managing the finances for her two startups over the past year. The profit from the first startup is represented by the equation 4x - 2x³, and the profit from the second startup is given by 5x³ - 4x + 5. Alice needs to calculate the combined annual profit from both startups.

• 3x³ + 5

• 3x³ + 8x + 5

• 3x² + 5

• 7x³ + 8x + 5

Subtract the polynomials. Enter the correct answer.

Mathematical Equivalence

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Simply:

• -1k⁴ +17k² +22

• -7k⁸ + 11k⁴-6

• -7k⁴ - 11k² +6

• 7k⁴ - 5k²

Bob and Sarah are planning to prepare two types of cookies for a local charity event. The first cookie recipe requires ingredients costing (2x² + 5x - 7) dollars, and the second cookie recipe requires ingredients costing (3 - 4x² + 6x) dollars. How much will the ingredients for both cookie types cost in total?

• 2x² + 3x +1

• -2x² - 11x -4

• 2x² + 5x -7

• -2x² + 11x -4

Lisa and John are comparing their savings over the year. Lisa's savings can be represented by the polynomial (3- 2x + 2x²), indicating her savings in thousands over x months, while John's savings are represented by (4x -5 +3x²), also in thousands over x months. Calculate the difference between Lisa's and John's savings. 

• x_² + 6x + 8

• 2x² + 5x - 7

• -x² -6x + 8

• -2x² + 11x - 4

Bob is planning to expand his orchard. He currently has
(3x² - 3x + 2) apple trees and plans to plant more. After planting (x² - 2x + 1) apple trees, how many apple trees will Bob have in total?

• A
  4x³-2x²+2

• B
  4x² - 5x + 3

• C
  -2x³+2x+2

• D
  4x³-2x²-2

Dr. Smith, a mathematician, is analyzing the growth patterns of two different species of plants over time. She models the growth of each species with polynomial equations and decides to compare their growth by subtracting the polynomial equation of species B from species A: (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