Polynomials Subtract From

Subtract the polynomials.

Subtract the polynomials.

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

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

What will the subtraction sign in between the polynomials do to the second polynomial?

• Change all of it's signs

• Nothing

• Change the sign of the first term

• 4g²-2g

• 4g²+4g-6

• 6g²+2g+6

• 4g²+2g

Subtract the polynomials. Enter the correct answer.

Mathematical Equivalence

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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

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