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Factor, Remainder and Factorisation

Question 4 Fa...

Question

Factorise:
(i) $12 x^{2} - 7 x + 1$
(ii) $2 x^{2} + 7 x + 3$
(iii) $6 x^{2} + 5 x - 6$
(iv) $3 x^{2} - x - 4$

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Solution

Lets factorize the given quadratic expressions by splitting their middle terms.
(i) $12 x^{2} - 7 x + 1$
$12 x^{2} - 7 x + 1$
$= 12 x^{2} - 4 x - 3 x + 1$
$= 4 x (3 x - 1) - 1 (3 x - 1)$
$= (4 x - 1) (3 x - 1)$

(ii) $2 x^{2} + 7 x + 3$
$2 x^{2} + 7 x + 3$
$= 2 x^{2} + 6 x + x + 3$
$= 2 x (x + 3) + 1 (x + 3)$
$= (2 x + 1) (x + 3)$

(iii) $6 x^{2} + 5 x - 6$
$6 x^{2} + 5 x - 6$
$= 6 x^{2} + 9 x - 4 x - 6$
$= 3 x (2 x + 3) - 2 (2 x + 3)$
$= (3 x - 2) (2 x + 3)$
(iv ) $3 x^{2} - x - 4$
$3 x^{2} - x - 4$
$= 3 x^{2} - 4 x + 3 x - 4$
$= x (3 x - 4) + 1 (3 x - 4)$
$= (x + 1) (3 x - 4)$

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Similar questions

12 x^{2} - 7 x + 1

2 x^{2} + 7 x + 3

6 x^{2} + 5 x - 6

3 x^{2} - x - 4

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