Worksheet: Dividing Polynomials by Binomials Using Factorization

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

Q1:

Find the value of 𝑘 that makes the expression 𝑥𝑘𝑥+30 divisible by 𝑥5.

Q2:

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

Q3:

What is the width of a rectangle whose area is 4𝑥32𝑥+6𝑥 cm2 and whose length is 8𝑥+3𝑥 cm?

  • A2𝑥4𝑥 cm
  • B2𝑥 cm
  • C2𝑥+4𝑥 cm
  • D4𝑥4𝑥 cm

Q4:

By factoring, find all the solutions to 𝑥𝑥14𝑥+24=0, given that (𝑥+4) is a factor of 𝑥𝑥14𝑥+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

Q5:

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 𝑦5 cm, and the perimeter is 34 cm.

Q6:

Knowing that the length of a rectangle is 2𝑥+5 and its area is 4𝑥+10𝑥+6𝑥+15, express the width of the rectangle algebraically.

  • A2𝑥3
  • B𝑥+3
  • C3𝑥+2
  • D2𝑥+3
  • E3𝑥2

Q7:

Knowing that the volume of a box is 10𝑥+30𝑥8𝑥24, its length is 2, and its width is 𝑥+3, express the height of the box algebraically.

  • A4𝑥5
  • B5𝑥2
  • C5𝑥+4
  • D5𝑥4
  • E4𝑥+5

Q8:

+50𝑎𝑏+38𝑎𝑏=21𝑎𝑏+25𝑏+19.

  • A42𝑎𝑏, 2𝑎𝑏
  • B40𝑎𝑏, 2𝑎𝑏
  • C42𝑎𝑏, 2𝑎𝑏
  • D40𝑎𝑏, 2𝑎𝑏

Q9:

Find the value of 𝑘 that makes the expression 𝑥𝑘𝑥+20 divisible by 𝑥5.

Q10:

Find the value of 𝑘 that makes the expression 𝑥𝑘𝑥18 divisible by 𝑥+2.

Q11:

The area of a triangle is 18𝑥+73𝑥+35 cm2 and its base is (2𝑥+7) cm. Write an expression for its height.

  • A(9𝑥+5) cm
  • B(18𝑥+10) cm
  • C(9𝑥+10) cm
  • D(18𝑥+5) cm

Q12:

The area of a triangle is 48𝑥+62𝑥+9 cm2 and its base is (8𝑥+9) cm. Write an expression for its height.

  • A(6𝑥+1) cm
  • B(12𝑥+2) cm
  • C(6𝑥+2) cm
  • D(12𝑥+1) cm

Q13:

What is the width of a rectangle whose area is 37𝑥+35𝑥+6𝑥 cm2 and whose length is 7𝑥+6𝑥 cm?

  • A𝑥+5𝑥 cm
  • B𝑥 cm
  • C𝑥5𝑥 cm
  • D37𝑥+5𝑥 cm

Q14:

What is the width of a rectangle whose area is 30𝑥+15𝑥+15𝑥 cm2 and whose length is 5𝑥+5𝑥 cm?

  • A3𝑥+3𝑥 cm
  • B3𝑥 cm
  • C3𝑥3𝑥 cm
  • D30𝑥+3𝑥 cm

Q15:

A rectangle has an area of 𝑦+10𝑦+7𝑦+70 cm2 and a width of (𝑦+10) cm. Find its length in terms of 𝑦 and its perimeter when 𝑦=2.

  • AThe length is (𝑦+7) cm, and the perimeter is 21 cm.
  • BThe length is 𝑦+7 cm, and the perimeter is 46 cm.
  • CThe length is (𝑦+7) cm, and the perimeter is 42 cm.
  • DThe length is 𝑦+7 cm, and the perimeter is 132 cm.
  • EThe length is 𝑦+7 cm, and the perimeter is 46 cm.

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