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: ๐‘ฅโˆ’10๐‘ฅโˆ’7=(4๐‘ฅโˆ’7)()๏Šจ.

  • A8, 2๐‘ฅ+1
  • B2, 2๐‘ฅ+1
  • C4, 2๐‘ฅ+1
  • D8, 2๐‘ฅโˆ’1
  • E8, ๐‘ฅ+1

Q2:

Complete the following: 9๐‘ฅ+32๐‘ฅ๐‘ฆ+=(๐‘ฅ+4๐‘ฆ)()๏Šจ.

  • Aโˆ’16๐‘ฆ๏Šจ, 9๐‘ฅโˆ’4๐‘ฆ
  • B16๐‘ฆ๏Šจ, 4๐‘ฅ+9๐‘ฆ
  • C16๐‘ฆ๏Šจ, 9๐‘ฅโˆ’4
  • Dโˆ’16, 4๐‘ฅ+9๐‘ฆ
  • Eโˆ’16, 9๐‘ฅโˆ’4๐‘ฆ

Q3:

Complete the factorization: 20๐‘ฅโˆ’21๐‘ฅ+4=(4๐‘ฅโˆ’โ‹ฏ)(โ‹ฏโˆ’โ‹ฏ)๏Šจ.

  • A(4๐‘ฅโˆ’1)(๐‘ฅโˆ’4)
  • B(4๐‘ฅโˆ’1)(5๐‘ฅโˆ’5)
  • C(4๐‘ฅโˆ’2)(5๐‘ฅโˆ’4)
  • D(4๐‘ฅโˆ’1)(5๐‘ฅโˆ’4)
  • E(4๐‘ฅโˆ’1)(2๐‘ฅโˆ’5)

Q4:

Complete the following: 8๐‘ฅ=(4๐‘ฅ+7๐‘ฆ)(+5๐‘ฆ)๏Šจ.

  • A+34๐‘ฅ๐‘ฆ+35๐‘ฆ๏Šจ, 2๐‘ฅ
  • B+34๐‘ฅ๐‘ฆ+35๐‘ฆ๏Šจ, 2
  • Cโˆ’34๐‘ฅ๐‘ฆ+35๐‘ฆ, 2๐‘ฅ๏Šจ
  • D+34๐‘ฅ๐‘ฆ+35, 2
  • E+35๐‘ฅ๐‘ฆ+34๐‘ฆ๏Šจ, 2

Q5:

Find the value of ๐‘Ž if (๐‘ฅโˆ’3๐‘ฆ)(โˆ’4๐‘ฅโˆ’๐‘ฆ)=โˆ’4๐‘ฅ+๐‘Ž๐‘ฅ๐‘ฆ+3๐‘ฆ๏Šจ๏Šจ.

Q6:

Factorize fully 4๐‘ฅ๏€น9๐‘ฅโˆ’๐‘ฆ๏…+๐‘ฆ๏Šจ๏Šจ๏Šจ๏Šช.

  • A๏€น6๐‘ฅโˆ’4๐‘ฅ๐‘ฆ+๐‘ฆ๏…๏€น6๐‘ฅ+4๐‘ฅ๐‘ฆ+๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • B๏€น6๐‘ฅโˆ’8๐‘ฅ๐‘ฆโˆ’๐‘ฆ๏…๏€น6๐‘ฅโˆ’8๐‘ฅ๐‘ฆโˆ’๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • C๏€น6๐‘ฅโˆ’4๐‘ฅ๐‘ฆโˆ’๐‘ฆ๏…๏€น6๐‘ฅ+4๐‘ฅ๐‘ฆโˆ’๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • D๏€น6๐‘ฅโˆ’4๐‘ฅ๐‘ฆโˆ’๐‘ฆ๏…๏€น6๐‘ฅ+4๐‘ฅ๐‘ฆโˆ’๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ
  • E๏€น6๐‘ฅโˆ’8๐‘ฅ๐‘ฆ+๐‘ฆ๏…๏€น6๐‘ฅ+8๐‘ฅ๐‘ฆ+๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ

Q7:

Factorize fully 16๐‘ฅ+48๐‘ฅ๐‘ฆโˆ’64๐‘ฆ๏Šฎ๏Šช๏Šช๏Šฎ.

  • A16๏€น๐‘ฅโˆ’2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏€น๐‘ฅ+2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…(๐‘ฅ+๐‘ฆ)(๐‘ฅโˆ’๐‘ฆ)๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ
  • B16๏€น๐‘ฅโˆ’2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏€น๐‘ฅ+2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏€น๐‘ฅ+๐‘ฆ๏…(๐‘ฅ+๐‘ฆ)(๐‘ฅโˆ’๐‘ฆ)๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ
  • C16๏€น๐‘ฅ+2๐‘ฅ๐‘ฆโˆ’2๐‘ฆ๏…๏€น๐‘ฅ+2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏€น๐‘ฅ+๐‘ฆ๏…(๐‘ฅ+๐‘ฆ)(๐‘ฅโˆ’๐‘ฆ)๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ
  • D4๏€น๐‘ฅโˆ’2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏€น๐‘ฅ+2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏€น๐‘ฅ+๐‘ฆ๏…(๐‘ฅ+๐‘ฆ)(๐‘ฅโˆ’๐‘ฆ)๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ
  • E4๏€น๐‘ฅโˆ’2๐‘ฅ๐‘ฆโˆ’2๐‘ฆ๏…๏€น๐‘ฅ+2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…(๐‘ฅ+๐‘ฆ)(๐‘ฅโˆ’๐‘ฆ)๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ

Q8:

Factorize fully 50๐‘ฅ+8๐‘ฆโˆ’48๐‘ฅ๐‘ฆ๏Šช๏Šช๏Šจ๏Šจ.

  • A2๏€น5๐‘ฅโˆ’4๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏€น5๐‘ฅ+4๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • B2๏€น5๐‘ฅโˆ’2๐‘ฅ๐‘ฆโˆ’2๐‘ฆ๏…๏€น5๐‘ฅ+2๐‘ฅ๐‘ฆโˆ’2๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • C2๏€น5๐‘ฅโˆ’4๐‘ฅ๐‘ฆโˆ’2๐‘ฆ๏…๏€น5๐‘ฅ+4๐‘ฅ๐‘ฆโˆ’2๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • D2๏€น5๐‘ฅโˆ’2๐‘ฅ๐‘ฆโˆ’2๐‘ฆ๏…๏€น5๐‘ฅ+2๐‘ฅ๐‘ฆโˆ’2๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ
  • E2๏€น5๐‘ฅโˆ’2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏€น5๐‘ฅ+2๐‘ฅ๐‘ฆ+2๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ

Q9:

Factorize fully 25๐‘ฅ+16๐‘ฆ+36๐‘ฅ๐‘ฆ๏Šช๏Šช๏Šจ๏Šจ.

  • A๏€น5๐‘ฅโˆ’4๐‘ฅ๐‘ฆโˆ’4๐‘ฆ๏…๏Šจ๏Šจ๏Šจ
  • B๏€น5๐‘ฅโˆ’2๐‘ฅ๐‘ฆ+4๐‘ฆ๏…๏€น5๐‘ฅ+2๐‘ฅ๐‘ฆ+4๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • C๏€น5๐‘ฅโˆ’4๐‘ฅ๐‘ฆ+4๐‘ฆ๏…๏€น5๐‘ฅ+4๐‘ฅ๐‘ฆ+4๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • D๏€น5๐‘ฅโˆ’2๐‘ฅ๐‘ฆโˆ’4๐‘ฆ๏…๏€น5๐‘ฅ+2๐‘ฅ๐‘ฆโˆ’4๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ๏Šจ
  • E๏€น5๐‘ฅโˆ’2๐‘ฅ๐‘ฆโˆ’4๐‘ฆ๏…๏€น5๐‘ฅ+2๐‘ฅ๐‘ฆโˆ’4๐‘ฆ๏…๏Šจ๏Šจ๏Šจ๏Šจ

Q10:

Factorize fully โˆ’๐‘ฅ๐‘ฆ+33๐‘ฅ๐‘ฆ๐‘งโˆ’16๐‘ฅ๐‘ง๏Šช๏Šจ๏Šจ๏Šช.

  • A6๐‘ฅ๏€น๐‘ฆโˆ’๐‘ฆ๐‘งโˆ’๐‘ง๏…๏€น๐‘ฆโˆ’5๐‘ฆ๐‘งโˆ’2๐‘ง๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • B5๐‘ฅ๏€นโˆ’๐‘ฆ+5๐‘ฆ๐‘ง+๐‘ง๏…๏€นโˆ’๐‘ฆโˆ’5๐‘ฆ๐‘งโˆ’4๐‘ง๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • C๏€น๐‘ฆโˆ’๐‘ฆ๐‘งโˆ’๐‘ง๏…๏€น๐‘ฆโˆ’5๐‘ฆ๐‘งโˆ’2๐‘ง๏…๏Šจ๏Šจ๏Šจ๏Šจ
  • Dโˆ’๐‘ฅ๏€น๐‘ฆ+5๐‘ฆ๐‘งโˆ’4๐‘ง๏…๏€น๐‘ฆโˆ’5๐‘ฆ๐‘งโˆ’4๐‘ง๏…๏Šจ๏Šจ๏Šจ๏Šจ

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