Creating Polynomial Equations

Find the equation of a polynomial with roots 3, -2, and 5.

• (x - 3)(x - 2)(x - 5)

• (x + 3)(x - 2)(x - 5)

• (x - 3)(x + 2)(x - 5)

• (x - 3)(x + 2)(x + 5)

Write the equation of a polynomial with roots -5, 2, and 4.

• x ^3+x^2+22x-40 = 0

• -x ^3+x^2-22x-40= 0

• x ^3-x^2+22x-40 = 0

• x ^3 -x^2 - 22x + 40 = 0

What is the equation of a polynomial with roots -4, 0, and 2?

• (x - 4)(x - 0)(x - 2)

• (x + 4)(x + 0)(x + 2)

• (x + 4)x(x - 2)

• (x - 4)(x + 0)(x - 2)

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

Solve: -6x-1+5x²=8x²

• x = 5 ±√67 /6

• x = 1, 2/7

• x = 1 ±√ 22

• x = 3 ±√6 / -3

What are two solutions to the polynomial:
x²+14x=0

• x=0, x= 14

• x=-14

• x= 1, x =10

• x= -14, x = 0 

Solve x⁴ - 256 = 0

• x = 4, x = - 4

• x = 4, x = 4i

• x = 4, x -4, x = 4i

• x = 4, x -4, x = 4i,         x = -4i

Answer explanation

The roots of the polynomial equation can be found by factoring the equation as (x-1)(x+2)(x-3)=0. Therefore, x = 1, -2, 3.

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

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