Question

$factorise \: \: : \: {x}^{2} + 7x + 12$
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Answer 1

Answer:

$x {}^{2} + 7x + 12$

Step-by-step explanation:

ur ans is that

Answer 2

Answer :

• ( x + 3 )( x + 4 )

To do :

• Factorisation

Question :

• x² + 7x + 12

Solution :

• In above expression p = 7 and q = 12

we are to find two numbers a and b such that their sum is 7 and sum is 12

• i.e. a × b = 12, a + b = 7

Now let us look at the following manipulations :

• 1 × 12 = 12, 1 + 12 = 13
• 2 × 6 = 12, 2 + 6 = 8
• 3 × 4 = 12, 3 + 4 = 7

Select 3 and 4 for a and b respectively since the sum of 3 and 4 is equal to 7 which is coefficient of x and the product of 3 and 4 is equal to the constant term 12.

No other factors accept three and four satisfy the second relation.

Therefore,

• $\rm \green{ {x}^{2} + 7x + 12 }\\ \\ = {x}^{2} + (3 + 4)x + 3 \times 4 \\ = {x}^{2} + 3x + 4x + 3 \times 4 \\ = x(x + 3) + 4(x + 3) \\ \\ \rm \pink{= (x + 3)(x + 4)}$

$\therefore \: \rm{factorisation \: of \: \blue{{x}^{2} + 7x + 12}} \\ \\ \huge \implies \tt \red{(x + 3)(x + 4)}$