How do you factor the expression $x^{2} - 5 x - 14$ $x^2 - 5x - 14$ ?

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Answer 1 · 2016-04-07T09:24:38

$(x + 2) (x - 7)$ $(x + 2 ) ( x - 7)$ is the factorised form of the expression.

$x^{2} - 5 x - 14$ $x^2 - 5x - 14$

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

$N_{1} + N_{2} = b = - 5$ $N_1 +N_2 = b = - 5$

After trying out a few numbers we get $N_{1} = 2$ $N_1 = 2$ and $N_{2} = - 7$ $N_2 =-7$

$2 \cdot (- 7) = - 14$ $2*(-7) = -14$ , and $2 + (- 7) = - 5$ $2+(-7)= - 5$

$x^{2} - 5 x - 14 = x^{2} - 7 x + 2 x - 14$ $x^2 - 5x - 14 = x^2 - 7x + 2x - 14$

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

$(x - 7)$ $(x - 7)$ is a common factor to each of the terms

$(x + 2) (x - 7)$ $(x + 2 ) ( x - 7)$ is the factorised form of the expression.

How do you factor the expression x2−5x−14x^2 - 5x - 14?