How do you factor $2 x^{2} + 5 x + 2$ $2x^2+5x+2$ ?

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How do you factor $2 x^{2} + 5 x + 2$ $2x^2+5x+2$ ?

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Answer 1 · 2015-06-02T05:22:26

$2 x^{2} + 5 x + 2$ $2x^2+5x+2$

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:
$N_{1} \cdot N_{2} = 2 \cdot 2 = 4$ $N_1*N_2 = 2*2 = 4$
and
$N_{1} + N_{2} = b = 5$ $N_1 +N_2 = b = 5$
After trying out a few numbers we get $N_{1} = 4$ $N_1 = 4$ and $N_{2} = 1$ $N_2 =1$
$4.1 = 4$ $4.1= 4$ , and $4 + 1 = 5$ $4+1= 5$

$2 x^{2} + 5 x + 2 = 2 x^{2} + 4 x + 1 x + 2$ $2x^2+5x+2 = 2x^2+4x + 1x+2$
$2 x (x + 2) + 1 (x + 2)$ $2x(x+2) +1(x+2)$

$(x + 2)$ $(x+2)$ is common to both the terms.

$(2 x + 1) (x + 2)$ $color(blue)(( 2x+1)(x+2)$ is the factorised form.

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How do you factor $2 x^{2} + 5 x + 2$ $2x^2+5x+2$ ?

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