Find a polynomial of the form

f(x) = ax3 + bx2 + cx + d

such that f(0) = −3, f(1) = 2, f(3) = 5, and f(4) = 0. (a graphing calculator is recommended.)

Step-by-step explanation:

We are given that

f(0)=-3,f(1)=2,f(3)=5 and f(4)=0

We have to find the polynomial

Substitute the value x=0 then ,we get

f(0)=d=-3

Substitute x=1 then we get

(equation I)

Substitute x=3 then we get

 (Equation II)

Substitute x=4 then we get

(Equation III)

Equation I multiply by 3 then subtract from equation II

(Equation IV)

Equation II multiply by 4 and equation III multiply by 3 and subtract equation II from III

(Equation V)

Equation IV multiply by 2 and then subtract from equation V

Substitute the value of a in equation IV then we get

Substitute the value of b in equation I then we get

Substitute the values then we get

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