If p(t)=5t4+17t3–8t2+13t–12, use synthetic division to find p( – 4).

the value of this function p(t) at t = -4 is also 0

Step-by-step explanation:

Recall that synthetic division in a problem such as this one returns a remainder, which is sometimes zero and is sometimes not.  If not, then the remainder is the value of the given polynomial when evaluated at a given argument.  We are to determine the remainder here when t = -4:

Setting up synthetic division:

-4    /    5    17    -8    13    -12

                 -20   12   -16    12

           5      -3     4     -3      0

Since the remainder is 0, the value of this function p(t) at t = -4 is also 0.