How do you factor $x² + 14x + 40$ ?

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Answer 1 · 2015-07-04T15:33:17

$color(green)(=(x+4)(x+10)$

$x^2 + 14x +40$

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:

$N_1*N_2 = a*c = 1*40 = 40$
and,
$N_1 +N_2 = b = 14$

After trying out a few numbers we get $N_1 = 10$ and $N_2 =4$
$10*4 = 40$ , and $10 + 4= 14$

$x^2 + 14x +40 =x^2 + color(green)(10x + 4x) +40$

$=x(x+10) + 4(x+10)$
Here $(x+10)$ is common to both terms.

So the factorised form is $color(green)(=(x+4)(x+10)$

How do you factor x² + 14x + 40x² + 14x + 40?