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Factorisation Using Algebraic Identities

Factorize: ...

Question

Factorize: $8 x^{2} + 2 x - 3$

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Solution

Given, $8 x^{2} + 2 x - 3$

$= 8 x^{2} + 6 x - 4 x - 3$

$= 2 x (4 x + 3) - 1 (4 x + 3)$

$= (4 x + 3) (2 x - 1)$

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Q. Factorize the following polynomials.
(i) (x² – x)² – 8 (x² – x) + 12
(ii) (x – 5)² – (5x – 25) – 24
(iii) (x² – 6x)² – 8 (x² – 6x + 8) – 64
(iv) (x² – 2x + 3) (x² – 2x + 5) – 35
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(vi) (y² + 5y) (y² + 5y – 2) – 24
(vii) (x – 3) (x – 4)² (x – 5) – 6

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8 x^{2} + 2 x - 3 = 0

Factorize the following

8 x^{2} + 29 x - 12

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