Zeros of a polynomial and its factors, in both directions

Answer Key - Grade 11 Math Worksheet - Building Confidence

Circle the best answer, or write your answer on the line.

1. 1.

   Bo's robot plots p(x) = (x + 3)(x − 2)(x − 5). Which zero of p comes from the factor x + 3?

   -3
2. 2.

   Esme makes a table for p(x) = (x − 6)(x + 1)(x + 4) on graph paper. Which zero of p comes from the factor x − 6?

   6
3. 3.

   Jun marks the zero rows of p(x) = (x + 7)(x − 3)(x − 1). Which zero of p comes from the factor x + 7?

   -7
4. 4.

   Luz colors the zero rows of p(x) = (x − 3)²(x + 5) on a poster. Which list gives every zero of p with its multiplicity?

   • 3 and -5, each with multiplicity 1
   • -3 with multiplicity 2; 5 with multiplicity 1
   • 3 with multiplicity 2; -5 with multiplicity 1
   • 3 with multiplicity 1; -5 with multiplicity 2
5. 5.

   Milo's robot lists the zeros of p(x) = x²(x + 4)³. Which list gives every zero of p with its multiplicity?

   • 0 and -4, each with multiplicity 1
   • -4 with multiplicity 3
   • 0 with multiplicity 2; -4 with multiplicity 3
   • 0 with multiplicity 2; 4 with multiplicity 3
6. 6.

   Noah writes p(x) = (x + 6)(x − 2)⁴ on a math club card. Which list gives every zero of p with its multiplicity?

   • -6 with multiplicity 1; 2 with multiplicity 4
   • -6 and 2, each with multiplicity 1
   • -6 with multiplicity 4; 2 with multiplicity 1
   • 6 with multiplicity 1; -2 with multiplicity 4
7. 7.

   Ren checks p(x) = x(x − 7)² in a notebook. Which list gives every zero of p with its multiplicity?

   • 7 with multiplicity 2
   • 0 with multiplicity 1; 7 with multiplicity 2
   • 0 and 7, each with multiplicity 1
   • 0 with multiplicity 1; -7 with multiplicity 2
8. 8.

   x = -3, -2, -1, 0, 1, 2, 3; p(x) = 90, 96, 84, 60, 30, 0, -24. Tala's table for p(x) = x³ − 3x² − 28x + 60 has one row with output 0. Which factor of p does that row show?

   • x − 60
   • x + 2
   • x − 2
   • x − 1
9. 9.

   x = -3, -2, -1, 0, 1, 2, 3; p(x) = 28, 18, 0, -20, -36, -42, -32. Zee's robot prints a table for p(x) = x³ + 2x² − 19x − 20 with one zero row. Which factor of p does that row show?

   • x − 1
   • x
   • x + 20
   • x + 1
10. 10.

    x = -3, -2, -1, 0, 1, 2, 3; p(x) = -56, 0, 30, 40, 36, 24, 10. Esme colors the one zero row in a table for p(x) = x³ − 7x² + 2x + 40. Which factor of p does that row show?

    • x + 2
    • x − 40
    • x − 2
    • x + 1