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Grade 11 Polynomial Division & the Remainder Theorem Worksheet with Answers

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

Unit 3: PolynomialsPolynomial OperationsCCSS A-APR.B.2

Dividing polynomials by x − a and using the remainder and factor theorems. 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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Polynomial Division & the Remainder Theorem

Grade 11 · Math

Score___ / 12

Name

Class

Date

Learning goal: Polynomial Operations · CCSS A-APR.B.2

Directions: This worksheet has 2 parts. Read the instructions at the start of each part.

Example

Use the remainder theorem: what is the remainder when x^2 - 3x is divided by (x + 3)?

Answer: 18

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.
Part A

Yes or No? Tick one box for each.

YesNo
1Is (x + 4) a factor of x^2 + 3x - 18?
2Is (x + 5) a factor of x^2 + 10x + 25?
3Is (x - 6) a factor of x^2 - 12x + 36?
4Is (x - 6) a factor of x^2 - 3x - 18?
Part B

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

  1. 5

    Use the remainder theorem: what is the remainder when x^2 - 7x - 5 is divided by (x + 3)?

    Show your work
    Answer
  2. 6

    Use the remainder theorem: what is the remainder when x^2 - 8x - 5 is divided by (x - 4)?

    Show your work
    Answer
  3. 7

    Use the remainder theorem: what is the remainder when x^3 - 3x^2 + 7x - 2 is divided by (x + 2)?

    Show your work
    Answer
  4. 8

    Use the remainder theorem: what is the remainder when x^2 + x + 1 is divided by (x + 1)?

    Show your work
    Answer
  5. 9

    Use the remainder theorem: what is the remainder when 2x^3 + 3x^2 + 9x + 5 is divided by (x - 4)?

    Show your work
    Answer
  6. 10

    Use the remainder theorem: what is the remainder when x^2 - 6 is divided by (x - 2)?

    Show your work
    Answer
  7. 11

    Use the remainder theorem: what is the remainder when x^3 - 4x^2 + 7x + 3 is divided by (x - 4)?

    Show your work
    Answer
  8. 12

    Use the remainder theorem: what is the remainder when x^3 - 2x - 2 is divided by (x + 1)?

    Show your work
    Answer

★ Challenge corner for fast finishers

How many ways can a team of 3 be chosen from 9 students?

How did I do?

Teacher's comments

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

Answer key (click to show)
  1. 1.no
  2. 2.yes
  3. 3.yes
  4. 4.yes
  5. 5.25
  6. 6.-21
  7. 7.-36
  8. 8.1
  9. 9.217
  10. 10.-2
  11. 11.31
  12. 12.-1
  13. ★84 (challenge corner)

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