Zeros of a polynomial and its factors, in both directions

Answer Key - Grade 11 Math Worksheet - Challenge Me

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

1. 1.

   Luz sketches a polynomial with only the zeros -1 (multiplicity 2) and 3. It passes through (-2, -20). What is its leading coefficient?

   4
2. 2.

   Milo's robot draws a polynomial with only the zeros 2 (multiplicity 2) and -4, through (0, 48). What is its leading coefficient?

   3
3. 3.

   Ren draws a polynomial with only the zeros -2 (multiplicity 2) and 5, through (1, 108). What is its leading coefficient?

   -3
4. 4.

   Tala knows x = 1 is a zero of p(x) = x³ − 4x² − 7x + 10. What are all the zeros of p?

   -2, 1, 5
5. 5.

   Zee's robot reports that x = -3 is a zero of p(x) = x³ − 3x² − 10x + 24. What are all the zeros of p?

   -3, 2, 4
6. 6.

   Esme reads that x = -1 is a zero of p(x) = x⁴ − 2x³ − 7x² + 8x + 12. What are all the zeros of p?

   -2, -1, 2, 3
7. 7.

   Jun builds a polynomial with leading coefficient 1 and only the zeros 2 (multiplicity 2) and -3. What is it in standard form?

   x³ − x² − 8x + 12
8. 8.

   Kira's robot needs a polynomial with leading coefficient 2 and only the zeros -1 (multiplicity 2) and 4. What is it in standard form?

   2x³ − 4x² − 14x − 8
9. 9.

   Luz needs a polynomial with leading coefficient -1 and only the zeros 0 and 5 (multiplicity 2). What is it in standard form?

   -x³ + 10x² − 25x
10. 10.

    Milo writes a polynomial with leading coefficient 1 and only the zeros 1, -1 and 2 (multiplicity 2). What is it in standard form?

    x⁴ − 4x³ + 3x² + 4x − 4