Worksheet: Dividing Polynomials by Monomials

In this worksheet, we will practice dividing polynomials by monomials.

Q1:

Simplify 43𝑥+12𝑥6𝑥𝑥.

  • A43𝑥+12𝑥6𝑥
  • B43𝑥+12𝑥6𝑥
  • C43𝑥+12𝑥6𝑥
  • D43𝑥+12𝑥+6𝑥
  • E43𝑥12𝑥6𝑥

Q2:

Find the quotient of 26𝑎𝑏9𝑎𝑏𝑎𝑏.

  • A26𝑎𝑏9𝑎𝑏
  • B26𝑎𝑏9𝑎𝑏
  • C26𝑎𝑏+9𝑎𝑏
  • D26𝑎𝑏9𝑎𝑏

Q3:

Simplify 23𝑥𝑦+49𝑥𝑦+41𝑥𝑦𝑥𝑦.

  • A23𝑥𝑦+49𝑥𝑦41𝑥𝑦
  • B23𝑥𝑦49𝑥𝑦+41𝑥𝑦
  • C23𝑥𝑦49𝑥𝑦41𝑥𝑦
  • D23𝑥𝑦49𝑥𝑦41𝑥𝑦
  • E23𝑥𝑦49𝑥𝑦41𝑥𝑦

Q4:

Simplify 144𝑥+168𝑥+84𝑥12𝑥+3𝑥+19𝑥+18.

  • A15𝑥+33𝑥+25
  • B15𝑥+33𝑥+25
  • C9𝑥+5𝑥+11
  • D9𝑥+5𝑥+11

Q5:

What is the height of a rectangular prism whose volume is 17𝑥6𝑥𝑦 cm3 and whose base is a square of side 𝑥 cm?

  • A17𝑥6𝑥𝑦 cm
  • B17𝑥6𝑥𝑦 cm
  • C17𝑥6𝑦 cm
  • D17𝑥6𝑥𝑦 cm
  • E17𝑥6 cm

Q6:

Simplify 12𝑎11𝑎𝑏12𝑎𝑏2𝑎𝑏.

  • A66𝑎𝑏72𝑎𝑏
  • B130𝑎𝑏142𝑎𝑏
  • C66𝑎𝑏72𝑎𝑏
  • D130𝑎𝑏142𝑎𝑏

Q7:

What is the length of a rectangle whose area is 7𝑥𝑦+24𝑥𝑦+16𝑥𝑦 cm2 and whose width is 𝑥𝑦 cm?

  • A7𝑥𝑦+24𝑥𝑦+16𝑥𝑦 cm
  • B7𝑥𝑦+24𝑥𝑦+16𝑥𝑦 cm
  • C7𝑥𝑦24𝑥𝑦+16𝑥𝑦 cm
  • D7𝑥𝑦+24𝑥𝑦16𝑥𝑦 cm

Q8:

The area of a triangle is 12𝑥+4𝑥 cm2, and its base is 4𝑥 m. Write an expression for its height.

  • A48𝑥+16𝑥 cm
  • B(12𝑥+4) cm
  • C(3𝑥+1) cm
  • D(6𝑥+2) cm

Q9:

The area of the shaded region in the figure below is 3𝑥𝑦+10𝑥𝑦 cm2. By considering the areas of the rectangles 𝐴𝐵𝐶𝐷 and 𝑀𝐸𝑁𝐹, find the length of 𝐹𝑁.

  • A(9𝑥𝑦+86) cm
  • B(3𝑥𝑦+58) cm
  • C(3𝑥𝑦+38) cm
  • D(3𝑥𝑦+86) cm
  • E(9𝑥𝑦+38) cm

Q10:

What is the length of a rectangle whose area is 21𝑥𝑦+23𝑥𝑦+20𝑥𝑦 cm2 and whose width is 𝑥𝑦 cm?

  • A21𝑥𝑦+23𝑥𝑦+20𝑥𝑦 cm
  • B21𝑥𝑦+23𝑥𝑦+20𝑥𝑦 cm
  • C21𝑥𝑦23𝑥𝑦+20𝑥𝑦 cm
  • D21𝑥𝑦+23𝑥𝑦20𝑥𝑦 cm

Q11:

What is the length of a rectangle whose area is 6𝑥𝑦+27𝑥𝑦 cm2 and whose width is 𝑥𝑦 cm?

  • A6𝑥+27𝑥 cm
  • B6𝑥𝑦+27𝑥𝑦 cm
  • C6𝑥𝑦27𝑥𝑦 cm
  • D6𝑥27𝑥 cm

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