evaluate each function at the given value:
f(n)=-n^6+31n^4+26n^3+20n^2+-33n-20
when n=6
I was thinking that I should do synthetic division, but I've tried it a few times and I can't get it to work out correctly.
Please help!
To evaluate the function f(n) = -n^6 + 31n^4 + 26n^3 + 20n^2 - 33n - 20 at n = 6, you need to substitute 6 in place of n in the function and simplify the expression.
Let's substitute n = 6 into the expression:
f(6) = -(6)^6 + 31(6)^4 + 26(6)^3 + 20(6)^2 - 33(6) - 20
Simplifying the expression:
f(6) = -46656 + 31(1296) + 26(216) + 20(36) - 33(6) - 20
Multiply each term:
f(6) = -46656 + 40056 + 5616 + 720 - 198 - 20
Performing the additions and subtractions:
f(6) = -6538
Therefore, f(6) = -6538.
Synthetic division is a method used to divide a polynomial by a linear binomial of the form x - a. In this case, since you are evaluating the function at a specific value (n = 6), synthetic division is not necessary.
The procedure in this case is to substitute the given value (n = 6) into the function and simplify the expression using basic arithmetic operations.