How can you check to see if a value of x is a zero of the polynomial

  substitute that value for x in the polynomial and see if it evaluates to zero

Step-by-step explanation:

A "zero" of a polynomial is a value of the polynomial's variable that make the expression become zero when it is evaluated. As an almost trivial example, consider the polynomial x-3. The value x = 3 is a zero because substituting that value for x makes the expression evaluate as zero.

  3 -3 = 0

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Evaluating polynomials can be done different ways. Straight substitution for the variable is one way. Using synthetic division by x-a (where "a" is the value of interest) is another way. This latter method is completely equivalent to rewriting the polynomial to Horner form for evaluation.

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In the attachment, Horner Form is shown at the bottom.