How do you factor completely: $x^2 − 3x − 28$ ?

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Answer 1 · 2015-07-13T08:29:45

$=color(blue)((x+4)(x-7)$

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:

$N_1*N_2 = a*c = 1*-28 = -28$
and
$N_1 +N_2 = b = -3$

After trying out a few numbers we get $N_1 = -7$ and $N_2 =4$
$7*-4 = -28$ , and $4+(-7)= -3$

$x^2 -3x -28$
$=x^2 -7x +4x -28$
$=x(x-7)+ 4(x -7)$

$=color(blue)((x+4)(x-7)$

How do you factor completely: x^2 − 3x − 28x^2 − 3x − 28?