Worksheet: Factoring Monic Quadratics

In this worksheet, we will practice factoring quadratic expressions in the form x² + bx + c where the coefficient of the leading term is 1.

Q1:

Factorize fully 𝑥𝑥30.

  • A(𝑥+15)(𝑥2)
  • B(𝑥+5)(𝑥6)
  • C(𝑥5)(𝑥6)
  • D(𝑥5)(𝑥+6)

Q2:

Factorize fully 𝑥15𝑥𝑦+54𝑦.

  • A(𝑥9𝑦)(𝑥6𝑦)
  • B(𝑥18𝑦)(𝑥3𝑦)
  • C(𝑥+9𝑦)(𝑥+6𝑦)
  • D(𝑥+9𝑦)(𝑥6𝑦)

Q3:

Which of the following is equivalent to (𝑥3𝑦)(𝑥+3𝑦)(𝑥18𝑥𝑦+81𝑦)?

  • A𝑥9𝑦𝑥+9𝑦
  • B(𝑥3𝑦)(𝑥+3𝑦)
  • C𝑥9𝑦
  • D𝑥27𝑦𝑥+27𝑦
  • E𝑥27𝑦

Q4:

Factorize fully 𝑎+12𝑎𝑏+36𝑏36𝑐.

  • A(𝑎+144𝑏+6𝑐)(𝑎+144𝑏6𝑐)
  • B(𝑎+6𝑏+6𝑐)(𝑎+6𝑏6𝑐)
  • C(𝑎+6𝑏+6𝑐)(𝑎6𝑏6𝑐)
  • D(𝑎6𝑏+6𝑐)(𝑎6𝑏6𝑐)
  • E𝑎+6𝑏+6𝑐𝑎+6𝑏6𝑐

Q5:

Factorize fully 𝑥+3𝑥+2.

  • A(𝑥+1)(𝑥+3)
  • B(𝑥+2)(𝑥+1)
  • C(𝑥2)(𝑥+1)
  • D(𝑥2)(𝑥1)

Q6:

Factorize fully 𝑥5𝑥+6.

  • A(𝑥6)(𝑥1)
  • B(𝑥3)(𝑥2)
  • C(𝑥+3)(𝑥2)
  • D(𝑥+3)(𝑥+2)

Q7:

Factorize fully 𝑥+2𝑥35.

  • A(𝑥+1)(𝑥35)
  • B(𝑥5)(𝑥+7)
  • C(𝑥+5)(𝑥+7)
  • D(𝑥+5)(𝑥7)

Q8:

Factorize fully 𝑥5𝑥24.

  • A(𝑥+6)(𝑥4)
  • B(𝑥8)(𝑥+3)
  • C(𝑥+8)(𝑥+3)
  • D(𝑥+8)(𝑥3)

Q9:

Factorize fully 𝑥9𝑥+18.

  • A(𝑥18)(𝑥1)
  • B(𝑥3)(𝑥6)
  • C(𝑥+3)(𝑥6)
  • D(𝑥+3)(𝑥+6)

Q10:

Factorize fully 𝑥13𝑥+40.

  • A(𝑥10)(𝑥4)
  • B(𝑥5)(𝑥8)
  • C(𝑥+5)(𝑥8)
  • D(𝑥+5)(𝑥+8)

Q11:

Factorize fully 𝑥+8𝑥9.

  • A(𝑥3)(𝑥+3)
  • B(𝑥1)(𝑥+9)
  • C(𝑥+1)(𝑥+9)
  • D(𝑥+1)(𝑥9)

Q12:

Factorize fully 𝑥+5𝑥36.

  • A(𝑥+18)(𝑥2)
  • B(𝑥4)(𝑥+9)
  • C(𝑥+4)(𝑥+9)
  • D(𝑥+4)(𝑥9)

Q13:

Factorize fully 𝑥+3𝑥4.

  • A(𝑥2)(𝑥+2)
  • B(𝑥+4)(𝑥1)
  • C(𝑥4)(𝑥1)
  • D(𝑥4)(𝑥+1)

Q14:

Factorize fully 𝑥9𝑥𝑦+20𝑦.

  • A(𝑥4𝑦)(𝑥5𝑦)
  • B(𝑥10𝑦)(𝑥2𝑦)
  • C(𝑥+4𝑦)(𝑥+5𝑦)
  • D(𝑥+4𝑦)(𝑥5𝑦)

Q15:

Factorize fully 𝑥8𝑥𝑦9𝑦.

  • A(𝑥+𝑦)(𝑥9𝑦)
  • B(𝑥+3𝑦)(𝑥3𝑦)
  • C(𝑥𝑦)(𝑥+9𝑦)
  • D(𝑥𝑦)(𝑥9𝑦)

Q16:

Factor 𝑥+8𝑥+12.

  • A(𝑥+6)(𝑥+2)
  • B(𝑥6)(𝑥2)
  • C(𝑥+3)(𝑥+4)
  • D(𝑥6)(𝑥+2)
  • E(𝑥+3)(𝑥4)

Q17:

Factorize fully 𝑥+2𝑥63𝑥.

  • A𝑥(𝑥+7)(𝑥9)
  • B𝑥(𝑥21)(𝑥+3)
  • C𝑥(𝑥+7)(𝑥+9)
  • D𝑥(𝑥7)(𝑥+9)

Q18:

Factor 𝑥8𝑥20.

  • A(𝑥+2)(𝑥+10)
  • B(𝑥10)(𝑥+2)
  • C(𝑥2)(𝑥10)
  • D(𝑥+4)(𝑥5)
  • E(𝑥4)(𝑥+5)

Q19:

Factor 𝑥+8𝑥20.

  • A(𝑥4)(𝑥+5)
  • B(𝑥+10)(𝑥2)
  • C(𝑥2)(𝑥10)
  • D(𝑥4)(𝑥5)
  • E(𝑥+2)(𝑥+10)

Q20:

Factor 𝑥8𝑥+12.

  • A(𝑥+6)(𝑥+2)
  • B(𝑥3)(𝑥4)
  • C(𝑥+3)(𝑥+4)
  • D(𝑥6)(𝑥2)
  • E(𝑥+6)(𝑥2)

Q21:

Expand and simplify 𝑎(𝑎+9)+18, then factorize the result.

  • A𝑎+6𝑎+3
  • B(𝑎+18)(𝑎+1)
  • C(𝑎+6)(𝑎+3)
  • D(𝑎+9)(𝑎+2)

Q22:

Factorize fully 𝑥3𝑥70.

  • A𝑥7𝑥+10
  • B𝑥+5𝑥14
  • C𝑥+14𝑥5
  • D𝑥+7𝑥10
  • E𝑥+7𝑥10

Q23:

Factorize fully 𝑎+6𝑎10(𝑎+6).

  • A(𝑎+10)(𝑎6)
  • B(𝑎10)(𝑎+6)
  • C(𝑎+3)(𝑎20)
  • D𝑎10𝑎+6

Q24:

Complete the following: 𝑧+16=(𝑧+)(+2).

  • A6𝑧, 8, 𝑧
  • B6𝑧, 8, 8𝑧
  • C6𝑧, 8, 𝑧
  • D6𝑧, 14, 8𝑧
  • E6𝑧, 8, 𝑧

Q25:

Expand and simplify (𝑎5𝑏)(𝑎+5𝑏)+24𝑎𝑏, then factorize the result completely.

  • A(𝑎+1)(𝑎25)
  • B(𝑎1)(𝑎+25)
  • C(𝑎𝑏)(𝑎+25𝑏)
  • D(𝑎+5𝑏)(𝑎5𝑏)

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