The Oakwood Academy Factorising Quadratic Expressions (A4iii) (Including Difference of Two Squares; Factorising when coefficient of x2 >1) Page 1 The Oakwood Academy Q1. Factorise 3x² + 14x + 8 .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. Answer ............................................ (Total 2 marks) Q2.(a) Factorise 3n2 + 7n + 4 ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ Answer ...................................................................... (2) (b) Hence, or otherwise, write 374 as the product of its prime factors. ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ ........................................................................................................................ Answer ...................................................................... (2) (Total 4 marks) Page 2 The Oakwood Academy Q3.(a) Factorise x + 10x + 24 2 ......................................................................................................................... ......................................................................................................................... Answer ...................................................................... (2) (b) Hence or otherwise, solve x2 + 10x + 24 = 0 ......................................................................................................................... Answer ...................................................................... (1) (Total 3 marks) Q4.(a) Expand and simplify (2x + 1)(3x − 4) .......................................................................................................................... .......................................................................................................................... Answer ...................................................................... (2) (b) Factorise 6x2 − 23x − 4 ......................................................................................................................... ......................................................................................................................... Answer ...................................................................... (2) (Total 4 marks) Page 3 The Oakwood Academy Q5.(a) Factorise x −9 2 ......................................................................................................................... Answer ...................................................................... (1) (b) Hence, simplify fully ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... Answer ...................................................................... (3) (Total 4 marks) Q6. Factorise 9a2 − b2 ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... Answer ...................................................................... (Total 2 marks) Q7.(a) Show clearly that (x + 5)(x − 5) ≡ x − 25 2 ...................................................................................................................... ...................................................................................................................... (1) Page 4 The Oakwood Academy (b) Simplify ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... ...................................................................................................................... Answer ...................................................................... (3) (Total 4 marks) Q8. Simplify fully .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. Answer ...................................................................... (Total 4 marks) Page 5 The Oakwood Academy 5x2 + 14x − 24 = 0 Q9.Solve the equation ................................................................................................................................. ................................................................................................................................. ................................................................................................................................. ................................................................................................................................. Answer ...................................................................... (Total 3 marks) Q10. (a) Factorise fully 2x² − 2x − 40 .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer.............................................................................. (3) (b) Factorise fully (x + y)² + (x + y)(2x + 5y) .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer.............................................................................. (3) (Total 6 marks) Page 6 The Oakwood Academy Q11.Simplify .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. Answer ...................................................................... (Total 3 marks) Q12. (a) Factorise 3x − 13x − 10 2 .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ...................................................................... (2) (b) Simplify .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ...................................................................... (2) (Total 4 marks) Page 7 The Oakwood Academy Q13.Simplify .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. Answer ...................................................................... (Total 3 marks) Q14. (a) Factorise fully 3x² − 12 .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ............................................................................. (2) (b) Factorise 5x² + 4xy − 12y² .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ............................................................................. (3) (Total 5 marks) Page 8 The Oakwood Academy Q15. (a) Factorise fully 12c²d − 9d² .......................................................................................................................... .......................................................................................................................... Answer ............................................................................. (2) (b) Factorise fully (w + 4)³ − (w + 4)²(w + 1) .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ............................................................................. (3) (Total 5 marks) Q16. (a) Factorise fully 5m² − 20p² .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ............................................................................. (3) Page 9 The Oakwood Academy (b) You are given that p = 15 and 5m² − 20p² = 0 Using your answer to part (a), or otherwise, work out the values of m. .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... .......................................................................................................................... Answer ............................................................................. (2) (Total 5 marks) Page 10
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