Lesson Worksheet: Solving Polynomial Equations Mathematics

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In this worksheet, we will practice using different methods to solve polynomial equations.

Q1:

Find the solution set of 𝑥−1089=0 in ℝ.

  • A{−33}
  • B{0,33}
  • C{−33,33}
  • D{33}

Q2:

Factorize fully 9𝑚−64𝑛.

  • A11𝑚+𝑛𝑚−𝑛
  • B8𝑚+3𝑛8𝑚−3𝑛
  • C3𝑚+8𝑛3𝑚−8𝑛
  • D8𝑚−3𝑛
  • E(3𝑚−8𝑛)

Q3:

Factorize fully 64𝑥−81.

  • A(9𝑥+8)(9𝑥−8)
  • B(𝑥−72)
  • C(8𝑥+9)(8𝑥−9)
  • D(𝑥+72)(𝑥−72)
  • E(8𝑥−9)

Q4:

Factorize fully 9𝑥−121𝑦𝑧.

  • A(11𝑥+3𝑦𝑧)(11𝑥−3𝑦𝑧)
  • B(3𝑥−11𝑦𝑧)
  • C(3𝑥+11𝑦𝑧)(3𝑥−11𝑦𝑧)
  • D(11𝑥−3𝑦𝑧)
  • E14(𝑥+𝑦𝑧)(𝑥−𝑦𝑧)

Q5:

Factorize fully 16𝑧+49−65𝑧.

  • A4𝑧−3𝑧+7
  • B(4𝑧−7)(𝑧+1)(𝑧−1)
  • C4𝑧−3𝑧+74𝑧+3𝑧+7
  • D(4𝑧+7)(4𝑧−7)(𝑧+1)(𝑧−1)
  • E(4𝑧+7)(4𝑧−7)(𝑧−1)

Q6:

Factorize fully 𝑥𝑦−49𝑥𝑦.

  • A𝑥𝑦(𝑥+7𝑦)(𝑥−7𝑦)
  • B𝑥+7𝑦𝑥−7𝑦
  • C𝑥𝑦𝑥+7𝑦𝑥−7𝑦
  • D𝑥𝑦𝑥−7𝑦
  • E𝑥𝑦𝑥+7𝑦𝑥−7𝑦

Q7:

Factorize fully 100𝑥−121𝑦.

  • A(11𝑥−10𝑦)
  • B(11𝑥+10𝑦)(11𝑥−10𝑦)
  • C21(𝑥+𝑦)(𝑥−𝑦)
  • D(10𝑥−11𝑦)
  • E(10𝑥+11𝑦)(10𝑥−11𝑦)

Q8:

Factor the expression 4𝑎−9𝑏.

  • A(2𝑎+3𝑏)(2𝑎−3𝑏)
  • B(2𝑎+3𝑏)(2𝑎+3𝑏)
  • C(𝑎+3𝑏)(4𝑎−3𝑏)
  • D(2𝑎−3𝑏)(2𝑎−3𝑏)
  • E(4𝑎−3𝑏)(𝑎−3𝑏)

Q9:

Given that 𝑥 is in ℝ, find the value of 𝑥 which satisfies the following equation 3𝑥−6𝑥+9=0. Give your answer to the nearest hundredth.

  • A𝑥=1.26, 𝑥=3.00 or 𝑥=−3.00
  • B𝑥=1.41
  • C𝑥=1.26
  • D𝑥=1.26 or 𝑥=3.00

Q10:

By factoring, find all the solutions to 𝑥+2𝑥−17𝑥−18𝑥+72=0, given that (𝑥−3) and (𝑥+4) are factors of 𝑥+2𝑥−17𝑥−18𝑥+72.

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

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