Uses of Synthetic Division



Uses of Synthetic Division March 22, 2010

Use #1 - We have already found that synthetic division is a “short-hand” method of finding the

zeros of polynomials, using just the coefficients of the polynomial.

Ex – To show that [pic] is one root (zero) of [pic] use synthetic division to find that the last number is zero.

[pic]

Factor the depressed polynomial to find the other roots:

[pic]

These are called zeros because they are the values of x that make f(x) = 0 .

Therefore for this function, f (3) = 0.

Use #2 – Evaluate a function.

One way to find f (5) is to plug it into the polynomial [pic]

[pic]

Try using synthetic division. Put the 5 in the left box.

[pic]

Due tomorrow - A.32 p. 354 #22-27

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