Factorise the given quadratic equation

$x^{2} + 5 x + 6 = 0.$

$(x + 2) (x + 3)$

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$(x - 2) (x - 3)$

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$(x + 1) (x + 3)$

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$(x - 1) (x - 3)$

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Solution

The correct option is A
$(x + 2) (x + 3)$

Comparing $x^{2} + 5 x + 6 = 0$ with $a x^{2} + b x + c = 0$ ,
we get a = 1 , b = 5 and c = 6.

Now, we need to find two numbers whose product is 6 and whose sum is 5.

Pairs of numbers whose product is 6 are

$(1, 6), (- 1, - 6), (2, 3)$ and $(- 2, - 3)$

Of these pairs , the pair that gives the sum as 5 is $(2, 3) .$

We can rewrite the given quadratic equation as

$x^{2} + 5 x + 6 = x^{2} + 2 x + 3 x + 6$
$= x (x + 2) + 3 (x + 2)$
$= (x + 2) (x + 3)$

Hence, the required answer is $(x + 2) (x + 3)$ .

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(v)

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Q. Solve the following quadratic equations by factorization:

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Solve the following quadratic equation by factorization.
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Q. Factorise the expression

x^{3} - 6 x^{2} + 11 x - 6

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Factorise the given quadratic equation x2+5x+6=0.

Factorise the given quadratic equation

$x^{2} + 5 x + 6 = 0.$