How do you factor $y^2 - 2y - 3$ ?

Question

5724 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-03T08:43:32

$y^2 - 2y - 3$

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:

$N_1*N_2 = a*c = 1*-3 = -3$
and
$N_1 +N_2 = b = -2$

After trying out a few numbers we get $N_1 = -3$ and $N_2 =1$
$-3*1 = -3$ , and $1+(-3)= -2$

$y^2 - 2y - 3 = y^2 - 3y + y- 3$

$y^2 - 3y + y- 3 = y(y-3) + 1(y- 3)$

$(y-3)$ is a common factor to each of the terms

$=color(green)((y+1)(y-3)$

How do you factor y^2 - 2y - 3 y^2 - 2y - 3 ?