Question

Two athletes, Jack and Jill, invite you to participate in a 5K run with several hills. One hill can be represented by the function f(x) = 2x2 + 5. Another hill can be represented by the function g(x) = 2x2 - 3x + 4. Describe to Jack and Jill, using complete sentences, which of the operations—addition, subtraction, multiplication, and division—will result in the largest degree function and which operation will result in the smallest degree function.

Answer 1

they're 2x^2 not 2x2!

Answer 2

Multiplication of course will result in largest degree as shown below:
f(x) * g(x)
= (2x^2 + 5)(2x^2 - 3x + 4)
= 4x^4 - 6x^3 + 8x^2 + 10x^2 - 15x + 20
= 4x^4 - 6x^3 + 18x^2 - 15x + 20

The division results in lowest degree as follow:
(2x^2 + 5)(2x^2 - 3x + 4)
= 1 + (3x + 1)/(2x^2 - 3x + 4), where:
Quotient = 1 , Reminder = 3x + 1

I hope this helps

Answer 3

it does thank you!!

Answer 4

Anytime.