ax^2 + bx + c....how in the WORLD do you do these problems???

Switching sign has some fundamental formulas
1) '+' multiply by '+' gives '+'
2) '+' multiply by '-' gives '-'
3) '-' multiply by '-' gives '+'
Now can u figure out anything..?

OK.. It was at first (-5)(x^2 - 6x + 8). Simply factorize
(x^2 - 6x + 8)
= (x^2 - 4x - 2x + 8) [note: - 4x - 2x = -6x and (- 4x) (- 2x)=8x^2]
= x(x-4) - 2(x-4)
= (x-4)(x-2)
got it...?

Great story---let us try to answer !

First of all should be written as an equation :-
-5x² + 30x - 40 = 0
5x² - 30x + 40 = 0
x² - 6x + 8 = 0
(x - 4)(x - 2) = 0
x = 2 , x = 4

4x² + 20x - 24 = 0
x² + 5x - 6 = 0
(x + 6)(x - 1) = 0
x = - 6 , x = 1

- * + makes -
+ * - makes -
+ * + makes +
- * - makes +

-5(x - 4)(x - 2)
= -5(x*x - 4*x - 2*x + 4*2)
= -5(x^2 - 4x - 2x + 8)
= -5*x^2 + 5*4x + 5*2x - 5*8
= -5x^2 + 20x + 10x - 40
= -5x^2 + 30x - 40

Okay heres the answer to the second problem 4(x+6) (x-1)


I'll try to explain now....but idon't if i can.
First, u take out ne factors like u can take the 4 out and get
4(x^2+5-6). Then since it x^2 ur going to have (x ) (x ).
To fill in the those blanks u have to figure out what factors of -6=5. So 4(x+6) (x-1) = the problem 4(4x^2+5-6). U check ur answer by doing the butterfly method or w/e it is which is mulity the first to numbers in the () together which is x*x, then the first number by the last number x*-1. Then 2#*3# which is 6*x. Then last # in each () which is 6*-1. That part u mite need look up cuz it hard to xplain it on here.

But the answer is 4 (x+6) (x-1) = )
Hoped that help and didn't confuse u to much!

Whenever you factor, the first step is to factor out anything that all the terms have in common. Also, we always like the x^2 term to be positive. So, we factor a -5 out of all three terms (divide each term by -5, that's why the signs switch):
-5(x^2-6x+8).
Now find two numbers that multiply to get 8 (-4*-2=8) and add to get -6 (-4+-2=-6). If two numbers multiply and get a +, but add to get a -, they must both be negative:
-5(x-4)(x-2).

4(x^2+5x-6) 6*-1 = -6 6+-1 = 5
4(x+6)(x-1)

that's factoring and trinomials.

4x^2+20x-24

4(x^2+5x-6)

4(x+6)(x-1) is the answer i think


basically you take the greatest common factor (GCF) which is the largest number that will "factor" into all three terms. And since 4 is the largest number that goes into 4, 20 and 24, and there is no "x" in the last term, 4 is the only number or variable that you can factor out.

The rest is simple trinomial. you check by multiplying
4(x+6)(x-1) using the distribute method.

(use quadramatic equation) 4 first one
(2x-2)(2x+12)
2x=2 2x=-12
x=1 ou x= -6

This is a problem on factoring.

Given: -5x^2 + 30x - 40 Line 1

(-5)x^2 - (-5)6x + (-5) 8 Line 2

Explanation of Line 2:
If you just look at the numerical coefficients (disregarding
their signs), you will notice that 5 is the greatest common factor. Now, here we want to factor out 5 but we have to take note of the signs of each coefficient. Now, here is what
happened to each coefficient:
for - 5 well that is still -5;
for + 30 well that can be written in two ways: +5(+6) or
-5(-6). Remember you get positive in multiplication if
the signs of the two numbers are the same. So, which
one to choose? We choose -5(-6) so that we have -5
common with the first coefficient (-5)

Same thing happened to - 40. It can be written as
-5(8). So now you have Line 2: (-5)x^2 - (-5)6x + (-5) 8

(-5)(x^2 - 6x + 8) Line 3

Explanation of Line 3: From Line 2, we factor out -5, so the
result is Line 3.

(-5)(x - 4)(x - 2) Line 4
Explanation of Line 4:
Look at Line 3. You have the trinomial square x^2-6x+8.
Now, this trinomial square can be factored into two binomials.
and these two binomials are (x - 4) and (x - 2). You can verify this by multiplying (x - 4) by (x - 2). You will get x^2-6x+8.
Factoring trinomial square is a topic in Algebra and requires practice to do it. I suggest if this is still vague, you read an
introductory book in Algebra.

4x^2 + 20x - 24
Again this one involves factoring a trinomial square.
Look at the coefficients: 4, 20 and -24. Notice that 4 is the greatest common factor, so we can factor it out. Here is
what happens:
4(x^2 + 5x - 6)
Now, x^2 + 5x - 6 can be factored as two binomials.
You just think out: what two numbers when multiply will give -6 and when added will give +5. Well, I can think of - 6 and +1.
So, you now write the two binomial factors:
(x - 6)(x + 1)
Now, our are answer will look like this: 4(x - 6)(x + 1)

Hope this helps. Good luck. Just be patient and don't give up.

teddy boy