Advanced Factorising & Completing the Square — Questions

IGCSE Mathematics (0580) practice questions. Work through each question before checking the solutions page.

Question 1

[2](a)Factorise x² − 49.

Question 2

[2](a)Factorise x² + 7x + 12.

Question 3

[3](a)Write x² + 6x + 5 in the form (x + a)² + b, and hence state the minimum value of the expression.

Question 4

[2](a)Factorise x² − 16.

Question 5

[2](a)Factorise 2x² + 7x + 3.

Question 6

[3](a)Write x² − 4x − 1 in the form (x + a)² + b.

Question 7

[2](a)Factorise 3x² − 12.

Question 8

[2](a)Factorise x² − 9x + 20.

Question 9

[2](a)Solve x² − 4x − 1 = 0 using the completed-square form found above, giving your answer to 2 decimal places.

Question 10

[2](a)Factorise 5x² − 20 fully.

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