Find all zeros of ƒ(x) = x^3 + 2x^2 – x – 2. then determine the multiplicity at each zero. state whether the graph will touch or cross the x-axis at the zero.

Zeros: -2, 1, -1

Multiplicity of each zero is 1

The graph crosses the x-axisat each zero.

Step-by-step explanation:

Consider the polynomial function

First, factor this function:

The zero of the function is such value of x at which f(x)=0. Note that f(x)=0 when

This is possible when

Therefore, the function f(x) has three zeros. Each zero is of multiplicity 1 (because each factor has 1st degree)

This means that at each zero the function will crosss the x-axis. (The function will touch the x-axis at its zero when this zero has even multiplicity)

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step-by-step explanation: