How do you factor $6 x^{2} + 7 x + 2$ $6x^2+7x+2$ ?

Question

22931 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-05-04T08:50:23

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:

$N_{1} \cdot N_{2} = a \cdot c = 6 \cdot 2 = 12$ $N_1*N_2 = a*c = 6*2 = 12$
AND
$N_{1} + N_{2} = b = 7$ $N_1 +N_2 = b = 7$

After trying out a few numbers we get $N_{1} = 3$ $N_1 = 3$ and $N_{2} = 4$ $N_2 =4$

$3 \cdot 4 = 12$ $3*4 = 12$ , and $3 + 4 = 7$ $3+4= 7$

$6 x^{2} + 7 x + 2 = 6 x^{2} + 3 x + 4 x + 2$ $6x^2 + 7x + 2 = 6x^2 +3x + 4x + 2$

$= 3 x (2 x + 1) + 2 (2 x + 1)$ $= 3x(2x+1) + 2(2x+1)$

$2 x + 1$ $2x+1$ is a common factor to each of the terms

$= (2 x + 1) (3 x + 2)$ $=color(green)((2x+1)(3x+2)$

How do you factor 6x2+7x+26x^2+7x+2?