factoring help. i need to kno how...?

Question

first i have problems like this:
-6x2* + 36x +96
and im suppose to factor that

then ive got
48x2* -24x +3
and i have to factor and solve this

the 2's that have a * after then are subscripted, but i cant type that.. like 6x suared, is wat it says...

can anyone explain to me how to do this? i know there a 4 boxes all connected together like

box box
box box

but i still dont get this.. any help pease?

Answer 1

You should be okay now with -6x^2 + 36x + 96, from the previous answerer.

Take out the constant factor from 48x^2 - 24x + 3:
= 3 * (16x^2 - 8x + 1)

Now, using a question mark for something which is going to be either a plus or a minus sign, the possibilities for 16x^2 - 8x + 1 are:
1. (16x ? 1) * (x ? 1)
2. (8x ? 1) * (2x ? 1)
3. (4x ? 1) * (4x ? 1)
All of these when multiplied out will give the correct x^2 term and constant term, namely 16x^2 and 1, but what about the x term?
No.1 would give 16+1 or 16-1 or -16+1 or -16-1, no good.
No.2 would give 8+2 or 8-2 or -8+2 or -8-2, no good either.
No.3 will give 8 or 0 or -8, can do, but what do the question marks need to be? Yes, (4x - 1) * (4x - 1) is 16x^2 - 8x + 1, so we've done.

Sorry, I've never seen the box arrangement either. It might be a teaching aid for teachers who don't understand what they're teaching very well. It's certainly got nothing to do with real mathematics, so don't worry about it.

Answer 2

First take out the integer, if possible:

-6x^2 + 36x + 96 = -6(x^2 - 6x - 16)

Now you know this will look like -6(x - a)(x - b) if it factors. If you multiply this it looks like x^2 - (a + b)x + ab, so you need to find numbers such that ab = -16 and a + b = -6. Usually you can look at the ways of factoring the last number:
16 = 1*16 = 2*8 = 4*4 to find one with a difference of 6. In this case 8-2=6, so the answer is -6*(x - 8)(x + 2).

I don't know what the box method is you are referring to, sorry.

Answer 3

-6x^2 + 36x + 96 = -6(x^2 - 6x - 16) = -6(x - 8)(x + 2)

48x^2 - 24x + 3 = 3(16x^2 - 8x + 1) = 3(4x - 1)(4x -1) or 3(4x - 1)^2

Answer 4

X= -b+/- the square root of b2 -4ac divided by 2a