List the multiplicities of the zeroes of each of the following polynomials.

             P ( x ) = 5x⁵ - 20x⁴ + 5x3 + 50x2 - 20x - 40 = 5 ( x + 1)² ( x - 2)³

Solution

Already we've determined the zeroes of each of these in earlier work or examples in this section thus we won't redo that work.  In each case we will just write down the earlier found zeroes & then go back to the factored form of polynomial, look at the exponent on each term & give the multiplicity.

There are two zeroes for this polynomial : x= -1 with multiplicity 2 and x= 2 with multiplicity 3.