How do you factor $x^{2} + 3 x + 2$ $x^2 +3x +2$ ?

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How do you factor $x^{2} + 3 x + 2$ $x^2 +3x +2$ ?

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Answer 1 · 2015-05-23T09:16:52

$x^{2} + 3 x + 2$ $x^2 +3x +2$

We can Split the Middle Term of this expression to factorise it
In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot 2 = 2$ $N_1*N_2 = a*c = 1*2 = 2$
And,
$N_{1} + N_{2} = b = 3$ $N_1 +N_2 = b = 3$

After trying out a few numbers we get $N_{1} = 2$ $N_1 = 2$ and $N_{2} = 1$ $N_2 =1$
$2 \cdot 1 = 2$ $2*1 = 2$ and $2 + 1 = 3$ $2+1= 3$

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

$(x + 1) (x + 2)$ $color(green)((x+1))color(red)((x+2)$ , is the factorised form.

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How do you factor $x^{2} + 3 x + 2$ $x^2 +3x +2$ ?

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