Factorising Quadratics Worksheet

Vedic maths trick 35: Factorising quadratics · Set 22 · 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 − 12x + 32 =
2.x² − 81 =
3.x² + 2x − 3 =
4.x² − 6x − 16 =
5.x² + 11x + 30 =
6.x² − 15x + 54 =
7.x² − 3x − 28 =
8.3x² + 25x + 42 =
9.x² − 16x + 63 =
10.x² + 2x − 63 =
11.x² − 11x + 30 =
12.2x² − 17x + 21 =
13.x² − 6x − 7 =
14.3x² − 14x + 16 =
15.2x² + 27x + 81 =
16.x² + 9x + 8 =
17.x² − 9x + 20 =
18.x² + 7x + 12 =
19.x² − x − 56 =
20.x² + 3x + 2 =
21.x² − 11x + 28 =
22.3x² − x − 30 =
23.x² − 16x + 63 =
24.x² + x − 12 =
25.x² + 10x + 24 =
26.x² + 2x − 3 =
27.x² − 25 =
28.x² − 3x − 54 =
29.3x² − 11x + 8 =
30.2x² + 3x − 2 =
31.x² + 5x + 6 =
32.x² + 14x + 45 =
33.x² + x − 6 =
34.x² − 3x − 4 =
35.x² + 3x + 2 =
36.3x² − 13x + 14 =
37.3x² − 5x + 2 =
38.x² + 8x + 7 =
39.3x² − 8x − 16 =
40.3x² + 7x − 6 =

Answer key

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

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