Can anyone help me by explaining how this problem is solved?
6w^2 - 40w + 66

Question

Can anyone help me by explaining how this problem is solved? 
6w^2 - 40w + 66

anonymous · Answer

Take 2 common:

$$2(3w^2 - 20w + 33) \implies 2(3w^3 - 9w - 11w + 33) \implies 2(3w - 11 )(w-3)$$

anonymous · Answer

How did you get - 9w - 11w ?

anonymous · Answer

Splitting  the middle term:

-20w can be written as : -9w - 11w

-9 and -11 will add up to give -20 again..

anonymous · Answer

But why did you pick 9 and 11?

anonymous · Answer

What did you get when you multiply 3 with 33???

anonymous · Answer

99?

anonymous · Answer

YEs..

We have to choose now two numbers that sum = -20 and product = +99

See, (-9)*(-11) = 99 (First Condition)

-9 - 11 = -20   (second condition)

That is why I chose that..

anonymous · Answer

Oh.. ok.

anonymous · Answer

How do I apply these steps when I do other similar problems?

anonymous · Answer

In this general equation:

$$ax^2 + bx + c$$

Firstly multiply a and c = a*c

Now you have to chose two numbers that sum to give $b$ and product to give $ac$..