40f 6 (3 complete) Find the zeros for the polynomial function and give the multi

Question

40f 6 (3 complete) 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 tuns around t f(x)=x3 + 6x2-16x-96 Determine the zero(s), if they exist The zero(s) is/are (Type integers or decimals. Use a comma to separate answers as needed.) Determine the multiplicities of the zero(s),iIf they exist. Select the correct choice below and.if necessary, llin th answer box(es) within your choice A. There is one zero. The multiplicity of the zero is [] O B. There are three zeros. The multiplicity of the smallest zero isThe multiplicty of the largest zeroisThe muplicty of the fher zero s oc. There are two zeros. The multiplicity of the smallest zero is Temu plicity of the largest zero is Determine Simplify your answer.) (Simplify your answers.) (Simplify your answers.) the behavior of the function at each zero. Select the correct choice below and, if necessary, illin the answer boxes wthin your choice The graph touches the x-axis and turns around at x The graph crosses the x axis atxz (Type integers or decimals. Simplify your answers. Use a comma to separate answers as needed) A. O B. The graph crosses the x-axis at all zeros O C. The graph touches the x-axis and turns around at all zeros. lick to select your answer(s)

Explanation / Answer

f(x)=x3+6x2-16x-96 =x2(x+6)-16(x+6)=(x2-16)(x+6)

zeroes, x2-16=0 , x+6=0

x=-4 ,4, -6

The multiplicity of all of the zeroes is 1 And crosses the x axis at -4,4,-6 .

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