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Expansion of (a ± b ± c)²

Factorize :i...

Question

Factorize $:$
(i) $x^{2} + 5 x + 6 = 0$
(ii) $x^{2} - 5 x + 6 = 0$
(iii) $x^{2} + 5 x - 6 = 0$
(iv) $x^{2} - 5 x - 6 = 0$

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Solution

(i) $x^{2} + 5 x + 6 = 0$ [using mid term expansion]
$x^{2} + 3 x + 2 x + 6 = 0$
$x (x + 3) + 2 (x + 3) = 0$
$(x + 2) (x + 3) = 0$
$[x = - 2]$ & $[x = - 3]$

(ii) $x^{2} - 5 x + 6 = 0$ [using mid term expansion]
$x^{2} - 3 x - 2 x + 6 = 0$
$x (x - 3) - 2 (x - 3) = 0$
$(x - 2) (x - 3) = 0$
$[x = 2]$ & $[x = 3]$

(iii) $x^{2} + 5 x - 6 = 0$ [using mid term expansion]
$x^{2} - x + 6 x - 6 = 0$
$x (x - 1) + 6 (x - 1) = 0$
$(x + 6) (x - 1) = 0$
$[x = - 6]$ & $[x = 1]$

(iv) $x^{2} - 5 x - 6 = 0$ [using mid term expansion]
$x^{2} + x - 6 x - 6 = 0$
$x (x + 1) - 6 (x + 1) = 0$
$(x - 6) (x + 1) = 0$
$[x = 6]$ & $[x = - 1]$

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