+2653 Let f be a cubic polynomial such that f(0) = 5, f(2) = 8, f(3)=13, and f(7) = -5. What is the sum of the coefficients of f?
+84 well if we say the cubic is \(ax^3+bx^2+cx+d\) then we already know that d is 5 since 0+0+0+d is 5 from f(0) = 5.
8a+4b+2c+5 is 8 from f(2) = 8
27a+9b+3c+5 is 13 from f(3) = 13
343a+49b+7c+5 is -5 from f(7) = -5
now its just a system of equations. im too lazy to type it out so im just going to put the final solution. if you need me to show you the system of equation steps tell me.
so the final solution is \(\boxed{\frac{148}{21}}\). hopefully :P
