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Grade 11 Zeros of Polynomials Worksheet with Answers

Grade 11 (US) · Year 12 (UK) · Class 11 (India) · Math

Unit 3: PolynomialsZeros of PolynomialsCCSS A-APR.B.3

Finding zeros and their multiplicities from factored form, and counting zeros by degree. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Zeros of Polynomials

Grade 11 · Math

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Learning goal: Zeros of Polynomials · CCSS A-APR.B.3

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Find the zeros of f(x) = (x - 6)(x - 5).

Answer: 5, 6

RememberComplex numbers and polynomials

i= ii²= −1i³= −ii⁴= 1Powers of i repeat every 4.a + bi: real part a, imaginary part b(a + bi)(a − bi) = a² + b²Remainder theorem: f(x) ÷ (x − c)leaves remainder f(c).If f(c) = 0, then x = c is a zero.
  1. 1

    Find the zeros of f(x) = (x + 4)(x - 3)(x - 4).

    Answer
  2. 2

    Find the zeros of f(x) = (x - 4)(x - 6)(x - 1).

    Answer
  3. 3

    Find the zeros of f(x) = (x + 6)(x - 1)(x + 5).

    Answer
  4. 4

    How many complex zeros (counting multiplicity) does a polynomial of degree 3 have?

    Show your work
    Answer
  5. 5

    How many complex zeros (counting multiplicity) does a polynomial of degree 4 have?

    Show your work
    Answer
  6. 6

    How many complex zeros (counting multiplicity) does a polynomial of degree 2 have?

    Show your work
    Answer
  7. 7

    How many complex zeros (counting multiplicity) does a polynomial of degree 6 have?

    Show your work
    Answer
  8. 8

    How many complex zeros (counting multiplicity) does a polynomial of degree 5 have?

    Show your work
    Answer
  9. 9

    Find the zeros of f(x) = (x + 5)(x + 1)(x - 4).

    Answer
  10. 10

    Find the zeros of f(x) = (x - 5)x(x - 3).

    Answer
  11. 11

    Find the zeros of f(x) = (x + 2)(x - 4)(x + 1).

    Answer
  12. 12

    Find the zeros of f(x) = (x + 4)(x - 2)(x - 3).

    Answer

★ Challenge corner for fast finishers

If a + b = 15 and ab = 24, what is a^2 + b^2?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/11/poly_zeros

Answer key (click to show)
  1. 1.-4, 3, 4
  2. 2.1, 4, 6
  3. 3.-6, -5, 1
  4. 4.3
  5. 5.4
  6. 6.2
  7. 7.6
  8. 8.5
  9. 9.-5, -1, 4
  10. 10.0, 3, 5
  11. 11.-2, -1, 4
  12. 12.-4, 2, 3
  13. ★177 (challenge corner)

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