Lesson Worksheet: Dividing Polynomials by Binomials Using Factorization Mathematics

Practice

In this worksheet, we will practice dividing polynomials by binomials using factorization.

Question 1

Find the value of 𝑘 that makes the expression 𝑥−𝑘𝑥+30 divisible by 𝑥−5.

Question 2

The area of a triangle is 12𝑥+38𝑥+28 cm2 and its base is (2𝑥+4) cm. Write an expression for its height.

  • A(6𝑥+7) cm
  • B(12𝑥+14) cm
  • C(6𝑥+14) cm
  • D(12𝑥+7) cm

Question 3

What is the width of a rectangle whose area is 4𝑥−32𝑥+6𝑥 cm2 and whose length is 8𝑥+3𝑥 cm?

  • A2𝑥−4𝑥 cm
  • B2𝑥 cm
  • C2𝑥+4𝑥 cm
  • D4𝑥−4𝑥 cm

Question 4

By factoring, find all the solutions to 𝑥−𝑥−14𝑥+24=0, given that (𝑥+4) is a factor of 𝑥−𝑥−14𝑥+24.

  • A𝑥=−2, 𝑥=−3, 𝑥=−4
  • B𝑥=2, 𝑥=3, 𝑥=4
  • C𝑥=2, 𝑥=3, 𝑥=−4
  • D𝑥=−2, 𝑥=−3, 𝑥=4
  • E𝑥=2, 𝑥=−3, 𝑥=4

Question 5

A rectangle has an area of 𝑦+2𝑦+5𝑦+10 cm2 and a width of (𝑦+2) cm. Find its length in terms of 𝑦 and its perimeter when 𝑦=4.

  • AThe length is (𝑦+5) cm, and the perimeter is 15 cm.
  • BThe length is 𝑦+5 cm, and the perimeter is 54 cm.
  • CThe length is (𝑦+5) cm, and the perimeter is 30 cm.
  • DThe length is 𝑦+5 cm, and the perimeter is 126 cm.
  • EThe length is 𝑦−5 cm, and the perimeter is 34 cm.

Question 6

⋯+50𝑎𝑏+38𝑎𝑏⋯=−21𝑎𝑏+25𝑏+19.

  • A42𝑎𝑏, −2𝑎𝑏
  • B−40𝑎𝑏, 2𝑎𝑏
  • C−42𝑎𝑏, 2𝑎𝑏
  • D40𝑎𝑏, 2𝑎𝑏

Question 7

Simplify 2𝑥+5𝑥−3𝑥+3.

  • A𝑥+2
  • B2𝑥−1
  • C2𝑥+1
  • D𝑥−1
  • E𝑥−2

Question 8

Find the denominator of the fraction in this equation: 3𝑥+11𝑥+8⋯=𝑥+1.

  • A8𝑥−3
  • B3𝑥−8
  • C3𝑥+8
  • D𝑥+8
  • E8𝑥+3

Question 9

Divide 𝑥−9𝑥+18 by 𝑥−6.

  • A𝑥+2
  • B𝑥+3
  • C𝑥−3
  • D𝑥−2
  • E𝑥−6

This lesson includes 1 additional questions and 60 additional question variations for subscribers.

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