Question

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

Answer 1

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

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

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5 -3 4 -3 0

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