How do you factor $x^2-5x+6=0$ ?

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Answer 1 · 2016-04-30T17:37:02

$color(green)((x-3)(x-2)$ is the factorised form of the expression.

$x^2 - 5x + 6 = 0$

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:

$N_1*N_2 = a*c = 1*6 = 6$

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 $(-2) +(-3)= -5$

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

$= x (x-2) -3 (x -2 )$

$(x-2)$ is a common factor to each of the terms

$=color(green)((x-3)(x-2)$

How do you factor x^2-5x+6=0x^2-5x+6=0?