How do you write $6x^2+5x+1$ in factored form?

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Answer 1 · 2015-09-17T16:57:35

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

$6x^2+5x+1= 6x^2+3x+2x+1$

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

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

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