Lesson Worksheet: Factoring Nonmonic Quadratics Mathematics

In this worksheet, we will practice factoring quadratic expressions in the form ax² + bx + c where the coefficient of the leading term is greater than 1.

Q1:

Factorize fully 4𝑥32𝑥+28.

  • A4(𝑥+1)(𝑥+7)
  • B(4𝑥+1)(𝑥7)
  • C4(𝑥1)(𝑥7)
  • D4(𝑥1)(𝑥+7)

Q2:

Factorize fully 6𝑥19𝑥+10.

  • A(2𝑥+5)(3𝑥2)
  • B(2𝑥5)(3𝑥2)
  • C(2𝑥5)(3𝑥+2)
  • D(2𝑥+5)(3𝑥+2)
  • E(6𝑥5)(𝑥2)

Q3:

Factor 6𝑥19𝑥+10.

  • A(3𝑥2)(2𝑥5)
  • B(3𝑥2)(2𝑥+5)
  • C(3𝑥+2)(2𝑥+5)
  • D(3𝑥5)(2𝑥+2)
  • E(3𝑥5)(2𝑥2)

Q4:

Factor 6𝑥5𝑥4.

  • A(3𝑥2)(2𝑥+2)
  • B(3𝑥1)(2𝑥+4)
  • C(2𝑥+1)(3𝑥4)
  • D(2𝑥1)(3𝑥+4)
  • E(3𝑥+2)(2𝑥2)

Q5:

Factorize fully 64(𝑥+1)9(𝑥1).

  • A24(𝑥+1)(𝑥1)
  • B(5𝑥+11)(11𝑥+5)
  • C(11𝑥+8)(5𝑥+3)
  • D(11𝑥+11)(5𝑥+5)
  • E(8𝑥+11)(3𝑥+5)

Q6:

Factor 6𝑥𝑥12.

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

Q7:

Factorize fully (4𝑥+7)(5𝑥2).

  • A9(𝑥1)(11𝑥+12)
  • B(9𝑥+5)(11𝑥+9)
  • C(9𝑥+5)
  • D9(𝑥+1)(11𝑥+12)
  • E(9𝑥+5)(9𝑥)

Q8:

Complete the following: 𝑥10𝑥7=(4𝑥7)().

  • A8, 2𝑥+1
  • B2, 2𝑥+1
  • C4, 2𝑥+1
  • D8, 2𝑥1
  • E8, 𝑥+1

Q9:

Expand and simplify 6𝑥+𝑦(10𝑦19𝑥), then factorize the result.

  • A(6𝑥5𝑦)(𝑥2𝑦)
  • B(2𝑥+5𝑦)(3𝑥2𝑦)
  • C(2𝑥+5𝑦)(3𝑥+2𝑦)
  • D(2𝑥5𝑦)(3𝑥2𝑦)

Q10:

Factorize fully 𝑥+𝑥+12.

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

Q11:

Complete the following: 9𝑥+32𝑥𝑦+=(𝑥+4𝑦)().

  • A16𝑦, 9𝑥4𝑦
  • B16𝑦, 4𝑥+9𝑦
  • C16𝑦, 9𝑥4
  • D16, 4𝑥+9𝑦
  • E16, 9𝑥4𝑦

Q12:

Factorize fully 604(𝑥𝑦)(𝑥𝑦).

  • A(𝑥𝑦+10)(𝑥𝑦6)
  • B(𝑥+𝑦+4)(𝑥+𝑦15)
  • C(𝑥𝑦10)(𝑥𝑦+6)
  • D(𝑥𝑦+3)(𝑥𝑦20)
  • E(𝑥+𝑦+10)(𝑥+𝑦6)

Q13:

Complete the factorization: 20𝑥21𝑥+4=(4𝑥)().

  • A(4𝑥1)(𝑥4)
  • B(4𝑥1)(5𝑥5)
  • C(4𝑥2)(5𝑥4)
  • D(4𝑥1)(5𝑥4)
  • E(4𝑥1)(2𝑥5)

Q14:

Using factorization, find, in terms of 𝑥, the dimensions of a rectangle given that its area is 5𝑥+12𝑥+7 cm2, and then find its perimeter when 𝑥=4.

  • A(5𝑥1) cm and (𝑥+7) cm, 60 cm
  • B(5𝑥+7) cm and (𝑥+1) cm, 64 cm
  • C(5𝑥7) cm and (𝑥+1) cm, 36 cm
  • D(5𝑥1) cm and (𝑥7) cm, 32 cm

Q15:

Factorize fully 12𝑥𝑦26𝑥𝑦+12𝑥𝑦.

  • A𝑥𝑦(12𝑥3)(𝑥2)
  • B𝑥𝑦(4𝑥+3)(3𝑥2)
  • C2𝑦𝑥(2𝑦3)(3𝑦2)
  • D2𝑥𝑦(𝑦3)(6𝑦2)
  • E2𝑥𝑦(2𝑦+3)(3𝑦+2)

Q16:

Complete the following: 8𝑥=(4𝑥+7𝑦)(+5𝑦).

  • A+34𝑥𝑦+35𝑦, 2𝑥
  • B+34𝑥𝑦+35𝑦, 2
  • C34𝑥𝑦+35𝑦, 2𝑥
  • D+34𝑥𝑦+35, 2
  • E+35𝑥𝑦+34𝑦, 2

Q17:

Expand and simplify 15𝑥2𝑦(4𝑦7𝑥), then factorize the result completely.

  • A(3𝑥4𝑦)(5𝑥2𝑦)
  • B(3𝑥4𝑦)(5𝑥+2𝑦)
  • C(15𝑥+4𝑦)(𝑥2𝑦)
  • D(3𝑥+4𝑦)(5𝑥2𝑦)

Q18:

Factorize fully 3(2𝑥+3𝑦)+11(2𝑥+3𝑦)(2𝑥4𝑦)+6(2𝑥4𝑦).

  • A(𝑥3𝑦)(3𝑥2𝑦)
  • B(8𝑥9𝑦)(10𝑥+𝑦)
  • C(2𝑥+3𝑦)(2𝑥4𝑦)
  • D(8𝑥+9𝑦)(10𝑥𝑦)
  • E(𝑥+3𝑦)(3𝑥+2𝑦)

Q19:

Factorize fully 48𝑚+48𝑚𝑛15𝑛.

  • A34𝑚5𝑛4𝑚+𝑛
  • B34𝑚5𝑛4𝑚𝑛
  • C34𝑚𝑛4𝑚+5𝑛
  • D4𝑚𝑛4𝑚+5𝑛

Q20:

Factorize fully 6𝑥17𝑥+12𝑥.

  • A(6𝑥4)(𝑥3)
  • B𝑥(3𝑥+4)(2𝑥+3)
  • C𝑥(3𝑥4)(2𝑥+3)
  • D(3𝑥+4)(2𝑥3)
  • E𝑥(3𝑥4)(2𝑥3)

Q21:

Factorize fully 4524𝑥+48𝑥.

  • A(48𝑥+3)(𝑥5)
  • B3(4𝑥+3)(4𝑥5)
  • C3(4𝑥3)(4𝑥+5)
  • D3(4𝑥+3)(4𝑥+5)
  • E(12𝑥3)(4𝑥5)

Q22:

Which of the following is a factor of 2𝑥3𝑥2?

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

Q23:

Find the value of 𝑎 if (𝑥3𝑦)(4𝑥𝑦)=4𝑥+𝑎𝑥𝑦+3𝑦.

Q24:

Factorize fully 5𝑦+40𝑧+30𝑦𝑧.

  • A(5𝑦2𝑧)(𝑦+4𝑧)
  • B5(𝑦2𝑧)(𝑦4𝑧)
  • C5(𝑦+2𝑧)(𝑦4𝑧)
  • D5(𝑦+2𝑧)(𝑦+4𝑧)
  • E(5𝑦+𝑧)(𝑦+8𝑧)

Q25:

Factorize fully 4𝑥9𝑥𝑦+𝑦.

  • A6𝑥4𝑥𝑦+𝑦6𝑥+4𝑥𝑦+𝑦
  • B6𝑥8𝑥𝑦𝑦6𝑥8𝑥𝑦𝑦
  • C6𝑥4𝑥𝑦𝑦6𝑥+4𝑥𝑦𝑦
  • D6𝑥4𝑥𝑦𝑦6𝑥+4𝑥𝑦𝑦
  • E6𝑥8𝑥𝑦+𝑦6𝑥+8𝑥𝑦+𝑦

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