Factorising Quadratics Worksheet

Vedic maths trick 35: Factorising quadratics · Set 27 · 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 + 13x + 4 =
2.3x² + 17x − 56 =
3.x² − x − 6 =
4.x² − 5x + 6 =
5.2x² + 11x − 63 =
6.x² + 10x + 24 =
7.x² + 10x + 16 =
8.x² − 7x − 8 =
9.2x² + x − 45 =
10.x² − 2x − 8 =
11.x² − x − 72 =
12.x² − 2x − 48 =
13.2x² + 5x − 12 =
14.x² − 2x − 35 =
15.x² + 4x − 21 =
16.x² + 4x − 45 =
17.x² − 2x − 24 =
18.2x² + 7x − 30 =
19.x² − 2x − 15 =
20.x² + 2x − 35 =
21.3x² + 31x + 56 =
22.3x² + 13x + 12 =
23.x² − 13x + 42 =
24.x² + 8x − 9 =
25.3x² + 13x + 4 =
26.x² + 6x − 27 =
27.x² + 12x + 32 =
28.3x² − 20x + 12 =
29.x² − 3x − 10 =
30.x² − 14x + 45 =
31.x² + 2x − 15 =
32.x² − 6x + 8 =
33.2x² + x − 36 =
34.3x² + 2x − 16 =
35.x² + 4x − 5 =
36.x² + 9x + 8 =
37.2x² + 9x + 10 =
38.x² − 5x + 4 =
39.3x² − 37x + 90 =
40.x² − 4x − 12 =

Answer key

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

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