Success TutoringWorksheets

Year 12 Factorising and Solving Quadratics Worksheet — Level 2 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 12 quadratics worksheet.

Download answers PDFPrint answersBack to worksheet
Success TutoringWorksheetsAnswer sheetYear 12 · Mathematics · Quadratics

Year 12 Factorising and Solving Quadratics Worksheet — Level 2 — Practice Set 4 — Answers

Factorise, then use the null factor law.

1.Solve: x2 + 3x − 40 = 0

Answer: x = −8 or x = 5

  1. Factorise: (x + 8)(x − 5) = 0
  2. Null factor law: x + 8 = 0 or x − 5 = 0
  3. x = −8 or x = 5
2.Solve: x2 − 5x − 6 = 0

Answer: x = 6 or x = −1

  1. Factorise: (x − 6)(x + 1) = 0
  2. Null factor law: x − 6 = 0 or x + 1 = 0
  3. x = 6 or x = −1
3.Solve: x2 + 7x + 12 = 0

Answer: x = −4 or x = −3

  1. Factorise: (x + 4)(x + 3) = 0
  2. Null factor law: x + 4 = 0 or x + 3 = 0
  3. x = −4 or x = −3
4.Solve: x2 − 4x − 21 = 0

Answer: x = −3 or x = 7

  1. Factorise: (x + 3)(x − 7) = 0
  2. Null factor law: x + 3 = 0 or x − 7 = 0
  3. x = −3 or x = 7
5.Solve: x2 + 2x − 8 = 0

Answer: x = 2 or x = −4

  1. Factorise: (x − 2)(x + 4) = 0
  2. Null factor law: x − 2 = 0 or x + 4 = 0
  3. x = 2 or x = −4
6.Solve: x2 + 2x − 63 = 0

Answer: x = 7 or x = −9

  1. Factorise: (x − 7)(x + 9) = 0
  2. Null factor law: x − 7 = 0 or x + 9 = 0
  3. x = 7 or x = −9
7.Solve: x2 − 2x + 1 = 0

Answer: x = 1 or x = 1

  1. Factorise: (x − 1)(x − 1) = 0
  2. Null factor law: x − 1 = 0 or x − 1 = 0
  3. x = 1 or x = 1
8.Solve: x2 + 7x − 18 = 0

Answer: x = −9 or x = 2

  1. Factorise: (x + 9)(x − 2) = 0
  2. Null factor law: x + 9 = 0 or x − 2 = 0
  3. x = −9 or x = 2
9.Solve: x2 − 6x + 8 = 0

Answer: x = 4 or x = 2

  1. Factorise: (x − 4)(x − 2) = 0
  2. Null factor law: x − 4 = 0 or x − 2 = 0
  3. x = 4 or x = 2
10.Solve: x2 + 2x + 1 = 0

Answer: x = −1 or x = −1

  1. Factorise: (x + 1)(x + 1) = 0
  2. Null factor law: x + 1 = 0 or x + 1 = 0
  3. x = −1 or x = −1
Free worksheets at worksheets.successtutoring.com · © Success Tutoring · Free for personal and classroom use

Marking tips

  • Give credit for correct method even when the final answer slips — the working shows where the thinking went right.
  • For open-ended tasks, use the success criteria as a checklist rather than looking for one "right" answer.
  • Celebrate what went well first, then pick one thing to work on next.

Great work. Here's what to try next: