Factorising Quadratics Worksheet

Vedic maths trick 35: Factorising quadratics · Set 25 · 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

1.3x² − 22x + 35 =
2.3x² + 14x − 5 =
3.x² − 12x + 27 =
4.3x² − 13x + 10 =
5.x² + 13x + 36 =
6.x² − 8x + 12 =
7.x² + 8x − 9 =
8.2x² − 11x + 14 =
9.x² + 3x + 2 =
10.x² − x − 2 =
11.x² − 16x + 63 =
12.3x² − 17x − 28 =
13.3x² + 2x − 1 =
14.x² − 64 =
15.x² − 12x + 32 =
16.3x² − 16x + 20 =
17.x² − 11x + 18 =
18.2x² − 9x + 9 =
19.x² + 9x + 8 =
20.2x² − 13x − 7 =
21.x² − 6x − 7 =
22.x² + x − 6 =
23.x² + 6x − 7 =
24.x² + 15x + 56 =
25.3x² − 2x − 5 =
26.x² − 5x − 36 =
27.x² − 15x + 56 =
28.x² − x − 2 =
29.x² − 3x + 2 =
30.3x² + 25x − 18 =
31.x² + 2x − 3 =
32.3x² + 11x − 4 =
33.3x² + 22x + 24 =
34.3x² + 7x + 4 =
35.x² − 7x + 10 =
36.x² + 9x + 8 =
37.2x² + 5x − 3 =
38.3x² − 29x + 18 =
39.2x² − 3x − 2 =
40.x² + 3x − 4 =

Answer key

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

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