How do you factor $2 x^{2} + 3 x + 1$ $2x^2 + 3x + 1$ ?

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How do you factor $2 x^{2} + 3 x + 1$ $2x^2 + 3x + 1$ ?

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Answer 1 · 2015-05-28T14:57:07

$2 x^{2} + 3 x + 1$ $2x^2 + 3x + 1$

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:

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

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

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How do you factor $2 x^{2} + 3 x + 1$ $2x^2 + 3x + 1$ ?

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