The correct format of the question is
The value of a rare baseball card issued in 1989 is represented by the function f(x) = [tex]0.2x^3- 0.25x^2+3x +4[/tex] where x represents the number of years since the baseball card was issued. Use the Remainder Theorem to find the value of the card in 1999
Answer:
The value of the card in 1999 is 209
Step-by-step explanation:
The remainder theorem says that
If you divide a Polynomial by f(x) be a Linear factor of the form (x-a) the remainder will be equal to F(a).
f(x) = [tex]0.2x^3- 0.25x^2+3x +4[/tex]
So we need to find from 1989 to 1999 which is 10 years
so our a = 10
Factor will be x-10
Applying remainder theorem
[tex]\frac{ 0.2x^3 -0.25x^2+3x+4}{x-10}[/tex]
we will get
Quotient = [tex]0.2x^2 + 1.75x +20.5[/tex]
Remainder = 209
Verifying our result
F(10) = [tex]0.2(10)^3 -0.25(10)^2 + 3(10) + 4[/tex]
= 200 -25 + 30 + 4
= 209
