Factorising Quadratics Worksheet
The trick (Anurupyena): x² + bx + c: two numbers that multiply to c and add up to b → (x + one)(x + other). ax² + bx + c: multiply a × c; find two numbers that multiply to that and add up to b; split the middle term with them. Group the four terms in pairs and take out the common bracket. Check by multiplying back.
NameDateTime takenScore ___ / 40
- 1.x² − 25 =
- 2.2x² − 21x + 27 =
- 3.2x² − 11x + 9 =
- 4.2x² + 11x + 9 =
- 5.2x² − 3x + 1 =
- 6.2x² − 17x + 36 =
- 7.3x² + 19x − 14 =
- 8.x² + 11x + 18 =
- 9.x² − 4x − 45 =
- 10.x² − 6x − 7 =
- 11.x² − 2x − 15 =
- 12.2x² + 7x + 6 =
- 13.x² + 2x − 48 =
- 14.x² + 7x + 10 =
- 15.x² + 9x + 18 =
- 16.3x² − 2x − 1 =
- 17.x² − 7x − 18 =
- 18.2x² − 3x − 14 =
- 19.2x² − 27x + 81 =
- 20.x² + 2x − 8 =
- 21.3x² − 5x − 28 =
- 22.x² + 5x − 36 =
- 23.x² − 15x + 56 =
- 24.x² + 6x − 7 =
- 25.x² − x − 72 =
- 26.x² − 13x + 36 =
- 27.x² − 2x − 35 =
- 28.2x² + 17x + 21 =
- 29.3x² + 10x + 7 =
- 30.3x² + 14x − 24 =
- 31.x² − 2x − 48 =
- 32.x² − 6x − 7 =
- 33.x² − 12x + 35 =
- 34.x² + 9x + 8 =
- 35.3x² + 19x − 40 =
- 36.x² + 4x − 32 =
- 37.2x² − 5x + 3 =
- 38.x² + 15x + 56 =
- 39.x² − 11x + 30 =
- 40.2x² + 7x + 3 =
Answer key
- (x − 5)(x + 5)
- (2x − 3)(x − 9)
- (2x − 9)(x − 1)
- (2x + 9)(x + 1)
- (2x − 1)(x − 1)
- (2x − 9)(x − 4)
- (3x − 2)(x + 7)
- (x + 2)(x + 9)
- (x − 9)(x + 5)
- (x + 1)(x − 7)
- (x + 3)(x − 5)
- (2x + 3)(x + 2)
- (x − 6)(x + 8)
- (x + 2)(x + 5)
- (x + 6)(x + 3)
- (3x + 1)(x − 1)
- (x + 2)(x − 9)
- (2x − 7)(x + 2)
- (2x − 9)(x − 9)
- (x + 4)(x − 2)
- (3x + 7)(x − 4)
- (x − 4)(x + 9)
- (x − 8)(x − 7)
- (x − 1)(x + 7)
- (x − 9)(x + 8)
- (x − 9)(x − 4)
- (x + 5)(x − 7)
- (2x + 3)(x + 7)
- (3x + 7)(x + 1)
- (3x − 4)(x + 6)
- (x − 8)(x + 6)
- (x + 1)(x − 7)
- (x − 7)(x − 5)
- (x + 1)(x + 8)
- (3x − 5)(x + 8)
- (x + 8)(x − 4)
- (2x − 3)(x − 1)
- (x + 7)(x + 8)
- (x − 6)(x − 5)
- (2x + 1)(x + 3)
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