How do you factor $x^2 - 9x + 14$ ?

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Answer 1 · 2015-05-24T03:45:56

$x^2 - 9x + 14$

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:

$N_1*N_2 = a*c = 1*14 = 14$
and
$N_1 +N_2 = b = -9$

After trying out a few numbers we get $N_1 = -2$ and $N_2 =-7$
$(-2).(-7) = 14$ , and $(-2)+(-7)= -9$

$x^2 - 9x + 14 = x^2 - 7x - 2x + 14$

$= x(x-7) -2(x-7)$

$=color(green)((x-7)(x-2)$

How do you factor x^2 - 9x + 14 x^2 - 9x + 14 ?