How do you factor $3y^2 +13y + 4$ ?

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Answer 1 · 2016-02-26T15:40:28

$color(blue)((3y+1) (y+4)$ is the factorised form of the equation.

$3y^2 +13y +4$

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

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

$N_1*N_2 = a*c = 3*4 = 12$

AND

$N_1 +N_2 = b = 13$

After trying out a few numbers we get $N_1 = 12$ and $N_2 =1$
$12*1 = 12$ , and $12+ 1= 13$

$3y^2 +13y +4 =3y^2 +12y +y +4$

$=3y (y+4) + 1 (y+4)$

$(y+4)$ is a common factor to each of the terms.
$=(3y+1) (y+4)$

$color(blue)((3y+1) (y+4)$ is the factorised form of the equation.

How do you factor 3y^2 +13y + 43y^2 +13y + 4?