Worksheet: Dividing Polynomials by a Divisor of Second Degree or Higher

In this worksheet, we will practice dividing polynomials by divisors of the second degree or higher.

Q1:

We want to factor 3 5 𝑥 + 7 𝑥 4 2 𝑥 3 2 4 into two factors. Given that one of these factors is 𝑥 6 𝑥 2 , what is the other?

  • A 7 𝑥 2
  • B 3 5 𝑥 + 7 𝑥 2
  • C 7 𝑥 7 𝑥 2
  • D 7 𝑥 + 7 𝑥 2

Q2:

Find the quotient 𝑞 ( 𝑥 ) and the remainder 𝑟 ( 𝑥 ) when 4 𝑥 2 𝑥 3 𝑥 + 4 𝑥 5 7 6 4 is divided by 2 𝑥 2 𝑥 3 3 2 .

  • A 𝑞 ( 𝑥 ) = 1 1 𝑥 + 2 3 𝑥 2 + 7 2 and 𝑟 ( 𝑥 ) = 2 𝑥 + 𝑥 + 𝑥 + 5 𝑥 2 + 4 4 3 2
  • B 𝑞 ( 𝑥 ) = 2 𝑥 3 𝑥 + 6 𝑥 2 1 𝑥 2 + 1 5 4 3 2 and 𝑟 ( 𝑥 ) = 4 8 𝑥 + 7 1 𝑥 2 4 0 2
  • C 𝑞 ( 𝑥 ) = 4 8 𝑥 + 7 1 𝑥 2 4 0 2 and 𝑟 ( 𝑥 ) = 2 𝑥 3 𝑥 + 6 𝑥 2 1 𝑥 2 + 1 5 4 3 2
  • D 𝑞 ( 𝑥 ) = 2 𝑥 + 𝑥 + 𝑥 + 5 𝑥 2 + 4 4 3 2 and 𝑟 ( 𝑥 ) = 1 1 𝑥 + 2 3 𝑥 2 + 7 2
  • E 𝑞 ( 𝑥 ) = 2 𝑥 + 𝑥 + 𝑥 + 5 𝑥 2 + 4 4 3 2 and 𝑟 ( 𝑥 ) = 2 2 𝑥 + 2 3 𝑥 + 1 4 2

Q3:

Write 6 𝑥 3 𝑥 2 𝑥 + 3 𝑥 5 2 𝑥 3 𝑥 3 𝑥 4 in the form 𝑞 ( 𝑥 ) + 𝑟 ( 𝑥 ) 𝑑 ( 𝑥 ) .

  • A 3 𝑥 9 𝑥 2 9 𝑥 2 2 𝑥 + 2 7 4 + 2 4 𝑥 + + 3 2 2 𝑥 3 𝑥 3 𝑥 4
  • B 3 𝑥 + 9 𝑥 2 + 9 𝑥 2 + 6 𝑥 + 2 7 4 + 2 𝑥 3 𝑥 3 𝑥 4 2 4 𝑥 + + + + 2 2
  • C 3 𝑥 9 𝑥 2 9 𝑥 2 2 𝑥 + 2 7 4 + 2 𝑥 3 𝑥 3 𝑥 4 2 4 𝑥 + + 3 2
  • D 3 𝑥 + 9 𝑥 2 + 9 𝑥 2 + 6 𝑥 + 2 7 4 + 2 4 𝑥 + + + + 2 2 2 𝑥 3 𝑥 3 𝑥 4
  • E 3 𝑥 + 9 𝑥 2 + 9 𝑥 2 + 2 𝑥 + 2 7 4 + + + 2 4 𝑥 + 2 2 2 𝑥 3 𝑥 3 𝑥 4

Q4:

What is the width of a rectangle whose area is 𝑥 + 2 0 𝑥 + 1 6 𝑥 4 2 cm2 and whose length is 𝑥 + 4 𝑥 + 4 2 cm?

  • A 𝑥 4 𝑥 2 cm
  • B 𝑥 4 𝑥 2 cm
  • C 𝑥 + 4 𝑥 2 cm
  • D 𝑥 + 4 𝑥 2 cm

Q5:

Find the value of 𝑘 that makes the expression 3 9 𝑥 7 1 𝑥 5 1 𝑥 + 2 8 𝑥 5 4 𝑥 + 𝑘 4 3 2 6 divisible by 7 𝑥 6 𝑥 9 3 .

Q6:

Knowing that the volume of a cylinder is 𝜋 4 𝑥 + 1 2 𝑥 1 5 𝑥 5 0 3 2 and its radius is 2 𝑥 + 5 , express the height of the cylinder algebraically.

  • A 𝑥 1
  • B 𝑥 + 2
  • C 𝑥 + 1
  • D 𝑥 2
  • E 2 𝑥 2

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