Lesson Worksheet: Synthetic Division Mathematics • 10th Grade

In this worksheet, we will practice using synthetic division for dividing polynomials.

Q1:

Use synthetic division to divide 𝑥1 by 𝑥1.

  • A𝑥+1
  • B𝑥1
  • C𝑥+𝑥+1
  • D𝑥+𝑥1
  • E𝑥𝑥+1

Q2:

Use synthetic division to find the quotient when 𝑥+2𝑥3 is divided by 𝑥1.

  • A𝑥3𝑥+3
  • B𝑥+3𝑥+3
  • C𝑥𝑥+3
  • D𝑥𝑥3
  • E𝑥+𝑥+3

Q3:

Use synthetic division to find the remainder when 𝑥7𝑥+14𝑥6 is divided by 𝑥1.

Q4:

Use synthetic division to find the remainder when 𝑥2𝑥+4𝑥6 is divided by 𝑥1.

  • A3
  • B5𝑥8
  • C5
  • D5𝑥13
  • E5𝑥3

Q5:

Use synthetic division to simplify 6𝑥7𝑥+14𝑥62𝑥1.

  • A3𝑥2𝑥+6
  • B2𝑥+3𝑥+6
  • C3𝑥+2𝑥+6
  • D3𝑥2𝑥6
  • E2𝑥3𝑥6

Q6:

Use synthetic division to divide 𝑥5𝑥+4 by (𝑥+1)(𝑥2)(𝑥1).

  • A𝑥+2
  • B𝑥2
  • C𝑥+1
  • D𝑥+4
  • E𝑥1

Q7:

Look at the synthetic division provided.

Write the original polynomial is expanded form.

  • A𝑥5𝑥+2𝑥10𝑥𝑥5
  • B𝑥5𝑥2𝑥10𝑥+𝑥5
  • C𝑥+5𝑥2𝑥10𝑥+𝑥+5𝑥
  • D𝑥+5𝑥2𝑥10𝑥+𝑥+5
  • E5𝑥+𝑥+5𝑥2𝑥10𝑥+𝑥+5

Write the original polynomial in factored form.

  • A(𝑥5)(𝑥+1)(𝑥1)
  • B(𝑥+5)(𝑥+1)(𝑥1)
  • C(𝑥5)(𝑥+1)(𝑥1)
  • D(𝑥+5)(𝑥+1)(𝑥1)
  • E(𝑥+5)(𝑥+1)(𝑥1)

Q8:

Use synthetic division to divide 2𝑥+𝑥7𝑥+13 by 2𝑥1.

  • A𝑥+𝑥+7
  • B𝑥+𝑥3+102𝑥1
  • C𝑥+𝑥3102𝑥1
  • D𝑥+𝑥3
  • E𝑥+12𝑥72+132𝑥1

Q9:

Express the following synthetic division in the form 𝑁(𝑥)=𝑄(𝑥)𝐷(𝑥)+𝑅(𝑥).

  • A𝑥𝑥+2𝑥3𝑥+4𝑥+2=𝑥+𝑥+7𝑥+14𝑥2𝑥3+203
  • B𝑥𝑥+2𝑥3𝑥+4𝑥+2=𝑥+𝑥+7𝑥+14𝑥2𝑥3+53𝑥+44
  • C𝑥𝑥+2𝑥3𝑥+4𝑥+2=𝑥+𝑥+7𝑥+14𝑥+2𝑥3+53
  • D𝑥𝑥+2𝑥3𝑥+4𝑥+2=𝑥+𝑥+7𝑥+14𝑥+2𝑥3+44𝑥+53
  • E𝑥𝑥+2𝑥3𝑥+4𝑥+2=𝑥+𝑥+7𝑥+14𝑥2𝑥3+53𝑥+203

Q10:

Express the following synthetic division in the form 𝑁(𝑥)𝐷(𝑥)=𝑄(𝑥)+𝑅(𝑥)𝐷(𝑥).

  • A2𝑥+3𝑥2𝑥+4𝑥2𝑥+2=2𝑥+7𝑥+12𝑥+2854𝑥+2
  • B2𝑥+3𝑥2𝑥+4𝑥2𝑥2=2𝑥+7𝑥+12𝑥+28+54𝑥2
  • C2𝑥+3𝑥2𝑥+4𝑥2𝑥2=2𝑥+7𝑥+12𝑥+2854𝑥2
  • D2𝑥+3𝑥2𝑥+4𝑥2𝑥2=2𝑥7𝑥12𝑥28+54𝑥2
  • E2𝑥+3𝑥2𝑥+4𝑥2𝑥+2=2𝑥+7𝑥+12𝑥+28+54𝑥+2

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