Factorising Quadratics Worksheet

Vedic maths trick 35: Factorising quadratics · Set 60 · 40 sums

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 − 7x + 6 =
2.x² + 10x + 9 =
3.x² + 10x + 21 =
4.2x² − 3x − 35 =
5.2x² − 21x + 54 =
6.2x² + 23x + 45 =
7.x² + 4x + 3 =
8.x² − 5x − 6 =
9.x² + 13x + 40 =
10.3x² − 11x + 8 =
11.x² − 9x + 8 =
12.2x² − 15x + 27 =
13.x² − 8x − 9 =
14.x² − 9x + 20 =
15.x² + 4x + 3 =
16.x² − 3x − 28 =
17.3x² − 16x + 20 =
18.x² − x − 72 =
19.2x² + 5x + 3 =
20.x² − 13x + 36 =
21.x² − 17x + 72 =
22.3x² + 7x − 20 =
23.2x² − 5x − 42 =
24.x² + 6x + 5 =
25.x² + x − 30 =
26.x² + 4x − 12 =
27.2x² + 3x − 2 =
28.2x² − x − 1 =
29.x² − 49 =
30.x² − 10x + 9 =
31.x² − 3x − 54 =
32.3x² − 26x + 16 =
33.3x² − 28x + 9 =
34.x² − 4x − 5 =
35.3x² + 34x + 80 =
36.x² − 3x + 2 =
37.2x² − 17x + 35 =
38.x² − 2x − 15 =
39.x² + 14x + 48 =
40.x² − 64 =

Answer key

(x − 1)(x − 6)
(x + 1)(x + 9)
(x + 7)(x + 3)
(2x + 7)(x − 5)
(2x − 9)(x − 6)
(2x + 5)(x + 9)
(x + 1)(x + 3)
(x − 6)(x + 1)
(x + 5)(x + 8)
(3x − 8)(x − 1)
(x − 8)(x − 1)
(2x − 9)(x − 3)
(x + 1)(x − 9)
(x − 5)(x − 4)
(x + 3)(x + 1)
(x − 7)(x + 4)
(3x − 10)(x − 2)
(x + 8)(x − 9)
(2x + 3)(x + 1)
(x − 9)(x − 4)
(x − 9)(x − 8)
(3x − 5)(x + 4)
(2x + 7)(x − 6)
(x + 1)(x + 5)
(x − 5)(x + 6)
(x − 2)(x + 6)
(2x − 1)(x + 2)
(2x + 1)(x − 1)
(x − 7)(x + 7)
(x − 9)(x − 1)
(x + 6)(x − 9)
(3x − 2)(x − 8)
(3x − 1)(x − 9)
(x + 1)(x − 5)
(3x + 10)(x + 8)
(x − 1)(x − 2)
(2x − 7)(x − 5)
(x − 5)(x + 3)
(x + 6)(x + 8)
(x + 8)(x − 8)

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