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

Question

2144 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-12-03T07:59:27

$(2 x + 1) (x + 1)$ $color(blue)((2x+1)(x+1)$

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

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 $2 + 1 = 3$ $2+1= 3$

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

$= 2 x (x + 1) + 1 (x + 1)$ $=2x(x+1) +1(x+1)$

Here, $(x + 1)$ $(x+1)$ is common to both terms ,

$= (2 x + 1) (x + 1)$ $=(2x+1)(x+1)$

So, the factorised form of the equation is :
$(2 x + 1) (x + 1)$ $color(blue)((2x+1)(x+1)$

How do you factor the trinomial 2x2+3x+12x^2 + 3x + 1?