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 π‘₯βˆ’1 by π‘₯βˆ’1.

  • Aπ‘₯+1
  • Bπ‘₯βˆ’1
  • Cπ‘₯+π‘₯+1
  • Dπ‘₯+π‘₯βˆ’1
  • Eπ‘₯βˆ’π‘₯+1

Q2:

Use synthetic division to find the quotient when π‘₯+2π‘₯βˆ’3 is divided by π‘₯βˆ’1.

  • Aπ‘₯βˆ’3π‘₯+3
  • Bπ‘₯+3π‘₯+3
  • Cπ‘₯βˆ’π‘₯+3
  • Dπ‘₯βˆ’π‘₯βˆ’3
  • Eπ‘₯+π‘₯+3

Q3:

Use synthetic division to find the remainder when π‘₯βˆ’7π‘₯+14π‘₯βˆ’6 is divided by π‘₯βˆ’1.

Q4:

Use synthetic division to find the remainder when π‘₯βˆ’2π‘₯+4π‘₯βˆ’6 is divided by π‘₯βˆ’1.

  • Aβˆ’3
  • B5π‘₯βˆ’8
  • C5
  • D5π‘₯βˆ’13
  • E5π‘₯βˆ’3

Q5:

Use synthetic division to simplify 6π‘₯βˆ’7π‘₯+14π‘₯βˆ’62π‘₯βˆ’1.

  • A3π‘₯βˆ’2π‘₯+6
  • B2π‘₯+3π‘₯+6
  • C3π‘₯+2π‘₯+6
  • D3π‘₯βˆ’2π‘₯βˆ’6
  • E2π‘₯βˆ’3π‘₯βˆ’6

Q6:

Use synthetic division to divide π‘₯βˆ’5π‘₯+4οŠͺ by (π‘₯+1)(π‘₯βˆ’2)(π‘₯βˆ’1).

  • Aπ‘₯+2
  • Bπ‘₯βˆ’2
  • Cπ‘₯+1
  • Dπ‘₯+4
  • Eπ‘₯βˆ’1

Q7:

Look at the synthetic division provided.

Write the original polynomial is expanded form.

  • Aπ‘₯βˆ’5π‘₯+2π‘₯βˆ’10π‘₯βˆ’π‘₯βˆ’5οŠͺ
  • Bπ‘₯βˆ’5π‘₯βˆ’2π‘₯βˆ’10π‘₯+π‘₯βˆ’5οŠͺ
  • Cπ‘₯+5π‘₯βˆ’2π‘₯βˆ’10π‘₯+π‘₯+5π‘₯οŠͺ
  • Dπ‘₯+5π‘₯βˆ’2π‘₯βˆ’10π‘₯+π‘₯+5οŠͺ
  • Eβˆ’5π‘₯+π‘₯+5π‘₯βˆ’2π‘₯βˆ’10π‘₯+π‘₯+5οŠͺ

Write the original polynomial in factored form.

  • A(π‘₯βˆ’5)(π‘₯+1)(π‘₯βˆ’1)
  • B(π‘₯+5)(π‘₯+1)(π‘₯βˆ’1)
  • C(π‘₯βˆ’5)(π‘₯+1)(π‘₯βˆ’1)
  • D(π‘₯+5)(π‘₯+1)(π‘₯βˆ’1)
  • E(π‘₯+5)(π‘₯+1)(π‘₯βˆ’1)

Q8:

Use synthetic division to divide 2π‘₯+π‘₯βˆ’7π‘₯+13 by 2π‘₯βˆ’1.

  • Aπ‘₯+π‘₯+7
  • Bπ‘₯+π‘₯βˆ’3+102π‘₯βˆ’1
  • Cπ‘₯+π‘₯βˆ’3βˆ’102π‘₯βˆ’1
  • Dπ‘₯+π‘₯βˆ’3
  • Eπ‘₯+12π‘₯βˆ’72+132π‘₯βˆ’1

Q9:

Express the following synthetic division in the form 𝑁(π‘₯)=𝑄(π‘₯)𝐷(π‘₯)+𝑅(π‘₯).

  • Aπ‘₯βˆ’π‘₯+2π‘₯βˆ’3π‘₯+4π‘₯+2=ο€Ήπ‘₯+π‘₯+7π‘₯+14π‘₯βˆ’2π‘₯βˆ’3+203οŠͺ
  • Bπ‘₯βˆ’π‘₯+2π‘₯βˆ’3π‘₯+4π‘₯+2=ο€Ήπ‘₯+π‘₯+7π‘₯+14π‘₯βˆ’2π‘₯βˆ’3+53π‘₯+44οŠͺ
  • Cπ‘₯βˆ’π‘₯+2π‘₯βˆ’3π‘₯+4π‘₯+2=ο€Ήπ‘₯+π‘₯+7π‘₯+14π‘₯+2π‘₯βˆ’3+53οŠͺ
  • Dπ‘₯βˆ’π‘₯+2π‘₯βˆ’3π‘₯+4π‘₯+2=ο€Ήπ‘₯+π‘₯+7π‘₯+14π‘₯+2π‘₯βˆ’3+44π‘₯+53οŠͺ
  • Eπ‘₯βˆ’π‘₯+2π‘₯βˆ’3π‘₯+4π‘₯+2=ο€Ήπ‘₯+π‘₯+7π‘₯+14π‘₯βˆ’2π‘₯βˆ’3+53π‘₯+203οŠͺ

Q10:

Express the following synthetic division in the form 𝑁(π‘₯)𝐷(π‘₯)=𝑄(π‘₯)+𝑅(π‘₯)𝐷(π‘₯).

  • A2π‘₯+3π‘₯βˆ’2π‘₯+4π‘₯βˆ’2π‘₯+2=2π‘₯+7π‘₯+12π‘₯+28βˆ’54π‘₯+2οŠͺ
  • B2π‘₯+3π‘₯βˆ’2π‘₯+4π‘₯βˆ’2π‘₯βˆ’2=2π‘₯+7π‘₯+12π‘₯+28+54π‘₯βˆ’2οŠͺ
  • C2π‘₯+3π‘₯βˆ’2π‘₯+4π‘₯βˆ’2π‘₯βˆ’2=2π‘₯+7π‘₯+12π‘₯+28βˆ’54π‘₯βˆ’2οŠͺ
  • D2π‘₯+3π‘₯βˆ’2π‘₯+4π‘₯βˆ’2π‘₯βˆ’2=βˆ’2π‘₯βˆ’7π‘₯βˆ’12π‘₯βˆ’28+54π‘₯βˆ’2οŠͺ
  • E2π‘₯+3π‘₯βˆ’2π‘₯+4π‘₯βˆ’2π‘₯+2=2π‘₯+7π‘₯+12π‘₯+28+54π‘₯+2οŠͺ

Practice Means Progress

Download the Nagwa Practice app to access questions, unit-exams, and flashcards for your school courses.

scan me!

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.