How do you factor $6x^2 + 5x +1$ ?

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Answer 1 · 2015-09-23T12:52:20

$color(blue)( (2x+1) (3x +1 )$ is the factorised form of the expression.

$6x^2 +5x+1$

We can Split the Middle Term of this expression to factorise it.

In this technique, if we have to factorise an expression like $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_1*N_2 = a*c = 6*1 = 6$
AND
$N_1 +N_2 = b = 5$

After trying out a few numbers we get $N_1 = 2$ and $N_2 =3$
$2*3 =6$ and $2 + 3 = 5$

$6x^2 +color(blue)(5x)+1 = 6x^2 +color(blue)(2x+3x) +1$

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

$color(blue)( (2x+1) (3x +1 )$ is the factorised form of the expression.

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