Factorising Quadratics Worksheet

Vedic maths trick 35: Factorising quadratics · Set 36 · 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 − 4x − 45 =
2.x² − 10x + 9 =
3.3x² − 4x − 15 =
4.x² − 3x − 28 =
5.x² − 15x + 56 =
6.3x² − 19x + 20 =
7.x² + 3x − 18 =
8.x² − x − 30 =
9.x² + 8x − 9 =
10.3x² + 17x − 90 =
11.2x² − 15x − 27 =
12.x² − 8x + 15 =
13.3x² + 8x + 4 =
14.x² − 7x + 6 =
15.2x² + 9x − 56 =
16.x² − 14x + 45 =
17.x² + x − 56 =
18.2x² + x − 1 =
19.x² − x − 20 =
20.x² − 9 =
21.x² − 3x − 4 =
22.3x² + 26x − 9 =
23.2x² + x − 21 =
24.2x² + 13x + 18 =
25.3x² − 16x + 5 =
26.x² + 3x − 4 =
27.x² + 8x + 12 =
28.2x² − 11x − 21 =
29.x² + 3x − 54 =
30.x² + 3x − 40 =
31.3x² + 13x − 30 =
32.x² − 5x − 6 =
33.3x² − 28x + 60 =
34.x² − 8x + 15 =
35.x² − 4 =
36.2x² − 9x + 10 =
37.2x² + 3x − 14 =
38.x² + 4x − 12 =
39.x² + 4x − 45 =
40.2x² + 17x + 8 =

Answer key

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

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