Find the zeros for the polynomial function and give the multiplicity for each ze

Question

Find the zeros for the polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis or touches the x-axis and turns around, at each zero. f(x) = 3(x + 1 )(x + 2)3 A) -1, multiplicity 1, crosses x-axis; -2, multiplicity 3, crosses x-axis B)-1, multiplicity 1, crosses x-axis;-2, multiplicity 3, touches x-axis and turns around C) 1, multiplicity 1, touches x-axis; 2, multiplicity 3, touches x-axis and turns around D) 1, multiplicity 1, crosses x-axis; 2, multiplicity 3, crosses x-axis

Explanation / Answer

f(x)=3(x+1)(x+2)3

To find the zeroes, we have to set f(x) to zero and solve for x

3(x+1)(x+2)3=0

x+1=0, x+2=0

x=-1, x=-2

So the zeroes are -1 with a multiplicity of 1 and -2 with a multiplicity of 3.

Since both 1 and 3 are odd, therefore graph crosses the x axis .

Correct option is D

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