Suppose *f* is a polynomial such that* f(0)=47, f(1)=32, f(2)=-13, and f(3)=16*. What is the sum of the coefficients of *f*?

Rudram592 Apr 12, 2019

#1**+1 **

Since f(0) = 47.....this must be the constant term

And since f(1) = 32

The sum of the coefficients + 47 = 32 subtract 47 from both sides

Sum of the coefficients = 32 - 47 = -15

CPhill Apr 12, 2019

#4**+1 **

Mmmmm....

Let f(x) = ax^m + bx^n + cx^p + .......+ constant term

f(0) = a(0)^m + b(0)^n + c(0)^p + ......+ constant term = 47

The terms with coefficients all = 0....so the constant term must be 47

f(1) = a(1)^m + b(1)^n + c(1)^p + .......+ 47 = 32

The coefficient terms will just sum to the sum of their coefficients ...i.e., a + b + c + ......

So....

sum of coefficients + constant term = 32

sum of coefficients + 47 = 32

sum of coefficients = 32 - 47 = - 15

CPhill Apr 12, 2019