Question

Factorise x^2+4x+3 by using middle term splitting

Answer 1

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X² + 4X + 3




X² + 3X + X + 3



X ( X + 3 ) + 1 ( X + 3)


( X + 3) ( X + 1)



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Answer 2

${x}^{2} + 4x + 3 \\ = {x}^{2} + (1 + 3)x + 3 \\ = ( {x}^{2} + x )+(3x + 3 )\\ = x(x + 1) + 3(x + 1) \\ = (x + 1)(x + 3)$

Here,
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First step :

The first digit is x² means 1
The last digit is 3

So,
1×3

It can be said as (1+3)

♦ 4 is splitted into (1+3)
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Second Step :

Take brakets i.e. “(” & “)” In the first two digits and the last two digits.

That is,
x²+1+3x+3
=(x²+1)+(3x+3)
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Third step :

(1+3)x
= 1×x + 3×x
= x+3x

In,
(x²+x)+(3x+3)

here, x and 3 are common

So, x(x+1)+3(x+1)
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Fourth & last Step :

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

Here, (x+1) is common

The rest two digits x and 3
can be written as (x+3)

So, (x+1) (x+3)
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