Zeros and Multiplicity Worksheet with Answer Key

What's on the worksheet

1. Give each zero and multiplicity, and say if the graph crosses, touches or flattens.
   f(x) = (x - 4)^3(x + 2)^2g(x) = -x^4(x + 7)h(x) = (3 - x)^2(x + 1)^5k(x) = (4x + 12)^3m(x) = (x - 1)(x + 2)(x - 1)^2
2. Solve each polynomial inequality in interval notation, listing single points in braces.
   x^2(x - 3)^3(x + 2)^2 < 0(x + 1)^4(4 - x)(x - 2)^2 \le 0
3. Factor a cubic by grouping, then give zeros with multiplicity and the graph's position.
4. Decide whether the exponents a and b are even or odd from two function values.
5. Explain why a zero between two known values must have even multiplicity.
6. Read each zero's multiplicity from the graph and give the least possible degree.
7. Word problem: Amara's online shop profit rate over twelve months.