Worksheet: Factoring by Grouping

In this worksheet, we will practice factoring expressions by grouping.

Q1:

Factorize fully 𝑥+𝑥130.

  • A(𝑥5)𝑥+5𝑥+26
  • B(𝑥5)𝑥5𝑥+26
  • C(𝑥+5)𝑥+5𝑥+26
  • D(𝑥5)𝑥+5𝑥+25

Q2:

Factorize fully 𝑥2𝑥+5𝑥10.

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

Q3:

Factorize fully 𝑥+9𝑥8𝑥72.

  • A(𝑥8)𝑥+9
  • B𝑥+8𝑥+9
  • C𝑥8𝑥9
  • D𝑥8𝑥+9

Q4:

Factorize fully 𝑧+6𝑧+6+𝑧.

  • A𝑧+1(𝑧+6)
  • B(𝑧+1)𝑧+6
  • C𝑧+1𝑧+6
  • D(𝑧1)(𝑧+1)(𝑧+6)
  • E(𝑧1)𝑧+6

Q5:

Factorize fully 𝑥𝑦27𝑥𝑦+27.

  • A(𝑥1)(𝑥+1)𝑦+3
  • B(𝑥1)(𝑥+1)(𝑦+3)𝑦3𝑦+9
  • C(𝑥1)(𝑥+1)(𝑦3)𝑦3𝑦+9
  • D(𝑥1)(𝑥+1)(𝑦3)𝑦+3𝑦+9
  • E(𝑥1)(𝑥+1)𝑦3

Q6:

Expand 𝑎(𝑎16𝑏)+64𝑏81, and then factorize the result completely.

  • A(𝑎+8𝑏+9)(𝑎+8𝑏9)
  • B(𝑎8𝑏+9)(𝑎+8𝑏9)
  • C(𝑎8𝑏+9)(𝑎8𝑏9)
  • D(𝑎8𝑏9)
  • E(𝑎+9𝑏)(𝑎9𝑏)

Q7:

Factorize fully 𝑥𝑥𝑥+1.

  • A(𝑥1)(𝑥+1)𝑥𝑥+1
  • B(𝑥+1)(𝑥1)𝑥+𝑥+1
  • C𝑥+1(𝑥+1)𝑥+𝑥+1
  • D𝑥+1(𝑥1)𝑥+𝑥+1
  • E(𝑥1)(𝑥+1)𝑥+𝑥+1

Q8:

Expand and simplify 𝑎9𝑏+𝑎𝑏(𝑎9𝑏), then factorize the result.

  • A(𝑎3𝑏)
  • B(𝑎𝑏)(𝑎+3𝑏)(𝑎3𝑏)
  • C(𝑎+𝑏)(𝑎+3𝑏)(𝑎3𝑏)
  • D(𝑎+𝑏)(𝑎3𝑏)
  • E(𝑎+𝑏)(𝑎+3𝑏)

Q9:

Factorize fully 1𝑥+14𝑥𝑦49𝑦.

  • A(1+𝑥9𝑦)(1𝑥+9𝑦)
  • B(1+𝑥7𝑦)(1𝑥+7𝑦)
  • C(1+𝑥9𝑦)(1𝑥9𝑦)
  • D(1+𝑥7𝑦)(1𝑥7𝑦)

Q10:

Factorize fully 𝑎+𝑏+𝑎+𝑏.

  • A(𝑎+𝑏)𝑎𝑎𝑏+𝑏
  • B(𝑎+𝑏)𝑎𝑎𝑏+𝑏+1
  • C(𝑎+𝑏)𝑎+𝑎𝑏+𝑏1
  • D(𝑎𝑏)𝑎+𝑎𝑏+𝑏+1

Q11:

Factorize fully 𝑥+4𝑥𝑥4.

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

Q12:

Factorize fully 4𝑥(𝑥+2)16𝑥32𝑥.

  • A4𝑥(𝑥2)(𝑥+2)
  • B𝑥(𝑥2)(𝑥+2)
  • C4𝑥(𝑥+2)(𝑥2)
  • D4𝑥(𝑥+2)𝑥+4
  • E4𝑥(𝑥2)𝑥+4

Q13:

Factorize fully 𝑥(𝑦5)9𝑥(𝑦5)+18𝑦90.

  • A(𝑦5)(𝑥6)(𝑥3)
  • B(𝑦5)(𝑥+2)(𝑥+9)
  • C(𝑦5)(𝑥+1)(𝑥+18)
  • D(𝑦5)(𝑥+6)(𝑥+3)
  • E(𝑦+5)(𝑥6)(𝑥3)

Q14:

Factor the expression 3𝑝𝑛+1𝑛1 completely.

  • A𝑛(3𝑝1)+3𝑝1
  • B𝑛+1(3𝑝+1)
  • C(3𝑝1)𝑛+1
  • D𝑛1(3𝑝1)
  • E𝑛1(3𝑝+1)

Q15:

Factor the expression 𝑥(2𝑥+5)+2𝑥+5 completely.

  • A2𝑥(2𝑥+5)
  • B(𝑥+1)(2𝑥+5)
  • C(2𝑥+5)(𝑥+5)
  • D𝑥(2𝑥+5)
  • E(2𝑥+5)(𝑥+2)

Q16:

Factorize fully 𝑥+10𝑥+40𝑥+4𝑥.

  • A𝑥(𝑥10)𝑥+4
  • B𝑥+10𝑥+4
  • C𝑥(𝑥4)𝑥+10
  • D𝑥(𝑥+4)𝑥+10
  • E𝑥(𝑥+10)𝑥+4

Q17:

Factorize fully 4𝑥+8𝑥325𝑥𝑦+10𝑦.

  • A(𝑥2)(4𝑥+45𝑦)
  • B(𝑥2)(4𝑥45𝑦)
  • C(𝑥+2)(4𝑥+165𝑦)
  • D(𝑥2)(4𝑥+16+5𝑦)
  • E(𝑥2)(4𝑥+165𝑦)

Q18:

If 𝑎+20𝑏=11 and 𝑥+𝑦=3, what is the value of 𝑎𝑥+𝑎𝑦+20𝑏𝑥+20𝑏𝑦?

Q19:

Factorize fully 𝑧𝑏𝑧𝑥+𝑏𝑥.

  • A(𝑥+1)(𝑧𝑏)
  • B(𝑏+1)(𝑧𝑥)
  • C(𝑧+1)(𝑏𝑥)
  • D(𝑧1)(𝑥𝑏)
  • E(𝑥1)(𝑏𝑧)

Q20:

Factorize fully 4𝑥𝑎+𝑥𝑏+4𝑦𝑎+𝑦𝑏.

  • A(4𝑥+𝑦)(𝑎+𝑏)
  • B(4𝑥+𝑦)(4𝑎+𝑏)
  • C4(𝑥+𝑦)(𝑎+𝑏)
  • D(4𝑎+𝑏)(𝑥+𝑦)

Q21:

Factorize fully 5𝑧15𝑦𝑏𝑧+3𝑏𝑦.

  • A(3𝑧+𝑦)(𝑏5)
  • B(3𝑦𝑧)(𝑏5)
  • C(3𝑦+𝑧)(𝑏5)
  • D(3𝑦𝑧)(𝑏+5)
  • E(3𝑧𝑦)(𝑏5)

Q22:

Factorize fully 𝑦𝑥+4𝑥+6𝑦+24.

  • A(𝑥+4)(𝑦+6)
  • B(𝑦+4)(𝑥6)
  • C(𝑥4)(𝑦+6)
  • D(𝑦+4)(𝑥+6)
  • E(𝑦+4)(𝑥+24)

Q23:

Factorize fully 9𝑥𝑚4𝑙𝑧+4𝑙𝑥9𝑚𝑧.

  • A(𝑧𝑥)(9𝑚4𝑙)
  • B(𝑧𝑥)(9𝑚+4𝑙)
  • C(𝑥𝑧)(9𝑚4𝑙)
  • D(𝑥𝑧)(9𝑚+4𝑙)
  • E(𝑚𝑙)(9𝑥+4𝑧)

Q24:

Factorize fully 𝑥𝑦𝑛+𝑦𝑛𝑥𝑛1.

  • A(𝑦𝑛1)(𝑛+1)
  • B(𝑦𝑛1)(𝑥𝑛+1)
  • C(𝑥𝑛1)(𝑦𝑛+1)
  • D(𝑥𝑛1)(𝑦𝑛1)
  • E(𝑦𝑛1)(𝑥𝑛1)

Q25:

Factorize fully 𝑥𝑧+15𝑦𝑢3𝑧𝑦5𝑥𝑢.

  • A(𝑥3𝑦)(𝑢+5𝑧)
  • B(𝑦3𝑥)(𝑧5𝑢)
  • C(𝑥3𝑦)(𝑢5𝑧)
  • D(𝑥+3𝑦)(𝑧5𝑢)
  • E(𝑥3𝑦)(𝑧5𝑢)

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