How many roots does the polynomial function y=(x-2)(x+3)^2 have

3

Step-by-step explanation:

There is one root for each binomial factor.

... y = (x -2)(x +3)(x +3) . . . has 3 binomial factors

The roots are the values of x that make the factors be zero.

... (x -2) = 0 when x = 2

... (x +3) = 0 when x = -3

... (x +3) = 0 when x = -3

The root at x = -3 is said to have multiplicity 2.

Sometimes, we're concerned with the number of distinct roots. Since the three roots only have two different values, there are 2 distinct roots.

step-by-step explanation:

the options are kind of confusing. i can tell you what i see going on here when i look at the graph.

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