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

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

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Answer 1 · 2015-05-24T03:45:56

$x^{2} - 9 x + 14$ $x^2 - 9x + 14$

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

In this technique, if we have to factorise an expression like $a x^{2} + b x + c$ $ax^2 + bx + c$ , we need to think of 2 numbers such that:

$N_{1} \cdot N_{2} = a \cdot c = 1 \cdot 14 = 14$ $N_1*N_2 = a*c = 1*14 = 14$
and
$N_{1} + N_{2} = b = - 9$ $N_1 +N_2 = b = -9$

After trying out a few numbers we get $N_{1} = - 2$ $N_1 = -2$ and $N_{2} = - 7$ $N_2 =-7$
$(- 2) . (- 7) = 14$ $(-2).(-7) = 14$ , and $(- 2) + (- 7) = - 9$ $(-2)+(-7)= -9$

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

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

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

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

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