Lesson Worksheet: Factoring Nonmonic Quadratics Mathematics • 9th Grade

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:

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

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

Q2:

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

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

Q3:

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

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

Q4:

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

Q5:

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

Q6:

Factorize fully 4𝑥9𝑥𝑦+𝑦.

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

Q7:

Factorize fully 16𝑥+48𝑥𝑦64𝑦.

  • A16𝑥2𝑥𝑦+2𝑦𝑥+2𝑥𝑦+2𝑦(𝑥+𝑦)(𝑥𝑦)
  • B16𝑥2𝑥𝑦+2𝑦𝑥+2𝑥𝑦+2𝑦𝑥+𝑦(𝑥+𝑦)(𝑥𝑦)
  • C16𝑥+2𝑥𝑦2𝑦𝑥+2𝑥𝑦+2𝑦𝑥+𝑦(𝑥+𝑦)(𝑥𝑦)
  • D4𝑥2𝑥𝑦+2𝑦𝑥+2𝑥𝑦+2𝑦𝑥+𝑦(𝑥+𝑦)(𝑥𝑦)
  • E4𝑥2𝑥𝑦2𝑦𝑥+2𝑥𝑦+2𝑦(𝑥+𝑦)(𝑥𝑦)

Q8:

Factorize fully 50𝑥+8𝑦48𝑥𝑦.

  • A25𝑥4𝑥𝑦+2𝑦5𝑥+4𝑥𝑦+2𝑦
  • B25𝑥2𝑥𝑦2𝑦5𝑥+2𝑥𝑦2𝑦
  • C25𝑥4𝑥𝑦2𝑦5𝑥+4𝑥𝑦2𝑦
  • D25𝑥2𝑥𝑦2𝑦5𝑥+2𝑥𝑦2𝑦
  • E25𝑥2𝑥𝑦+2𝑦5𝑥+2𝑥𝑦+2𝑦

Q9:

Factorize fully 25𝑥+16𝑦+36𝑥𝑦.

  • A5𝑥4𝑥𝑦4𝑦
  • B5𝑥2𝑥𝑦+4𝑦5𝑥+2𝑥𝑦+4𝑦
  • C5𝑥4𝑥𝑦+4𝑦5𝑥+4𝑥𝑦+4𝑦
  • D5𝑥2𝑥𝑦4𝑦5𝑥+2𝑥𝑦4𝑦
  • E5𝑥2𝑥𝑦4𝑦5𝑥+2𝑥𝑦4𝑦

Q10:

Factorize fully 𝑥𝑦+33𝑥𝑦𝑧16𝑥𝑧.

  • A6𝑥𝑦𝑦𝑧𝑧𝑦5𝑦𝑧2𝑧
  • B5𝑥𝑦+5𝑦𝑧+𝑧𝑦5𝑦𝑧4𝑧
  • C𝑦𝑦𝑧𝑧𝑦5𝑦𝑧2𝑧
  • D𝑥𝑦+5𝑦𝑧4𝑧𝑦5𝑦𝑧4𝑧

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