5x^2+12x-9?

Question

5x^2+12x-9

I just need help understanding how you use the middle and the signs...

Answer 1

Okay, when you're choosing factors, the signs play the following roles:

The last sign (the -9) tells you whether the signs of your factors are the same or different. If the sign is a positive, the factors have the same signs; if it's a negative, the factors have different signs. Remember: this doesn't tell us whether the signs are positive/negative, just whether they're the same or different.

The first sign (the +12x) tells us the sign of the larger factor. If the sign is a positive, the largest factor is positive; if the sign is negative, the largest factor is negative. Here's an example:

x^2 + 4x + 3

Here, our factors are 3 and 1. The last sign (+3) tells us the factors have the same sign; the middle sign (+4x) tells us that the largest factor is positive. Thus, since the 3 is positive and they have the same sign, both must be positive and so we get:

(x+3)(x+1)

In your example, the factors we need are 3 and 3. So we know we have a:

(5x _ 3)(x _ 3)

Since the second sign is - (-9), your factors are going to have different signs; since your middle term is positive, your largest factor is positive (in this case, the largest is the one that will be multiplied by 5x since 5x*3 > x*3. Thus, we have:

(5x -3)(x+3)

Does that help?

Answer 2

You take factors of the first and last terms (5x^2 and 9) that add together to equal the middle term.

The only factors of 5x^2 are 5x and x, so you know that the first term in each set of parentheses is either 5x or x, so now we have

(5x +/- __?__) (x +/- __?__)

One of the middle signs has to be positive and one has to be negative because the last two terms in each set of parentheses need to multiply to equal -9.

The factors of -9 are +/-1, +/-3, and +/-9; for example, you could have a positive 1 in the first parentheses and a negative 9 in the second parentheses--multiplied together, they equal -9.

You're trying to get these factors of nine to combine with the factors of 5x^2 to get +12x in the middle. If you multiply +3 by the 5x, you get 15x, and -3 by the x, you get -3x, which add together to equal 12x, so the answer is:

(5x - 3)(x + 3)

If you multiply this equation out, you can see how it works:

5x^2 + 15x - 3x - 9
5x^2 + 12x - 9

Answer 3

Multiply Coef of x^2 and the constant term along with their respective signs. In this case the product is (+5).(-9) = (- 45)
Note whenever the product is negative. You have to break the middle term in to two factors whose difference is equal to the coeff of the middle term. In our case we have to factorize (-45) in two parts such that their difference is (+12). We get (+15 and - 3) . Here we see that their product is (-45) while their difference (algebric sum) is 12. Thus the given expression changes to :

5 x^2 + 15 x - 3 x - 9 = 5x ( x + 3 ) - 3 ( x + 3 )
= (5x - 3 ) ( x + 3 ) Answer

Answer 4

Um...no idea what you're looking for.

You can factor this as:
(5x-3)(x+3)

Is that what you want? To figure it out:

1. There is only one way to factor 5x² so we know 5x and x will be two terms of the factors.

2. The sign of the last term is negative, so we know that one of the other terms in the factors will be negative and one positive.

3. There are only two ways to fact 9 i.e 1*9 and 3*3.

4. To get +12, we have 5 * (1,3,9) and subtract 1 * (1,3,9). It's pretty easy to see that 5*3 + 1*-3 = +12.

Answer 5

I didn't understand totally what do you need... maybe it is just the equation and you need to find x1 and x2?
ok... so...
5x^2+12x-9=0
D=12^2+4*5*9=324
x1=((-12)+D^(0.5))/(2*5)=
=((-12)+18)/10=3/5
x2=((-12)-D^(0.5))/(2*5)=
=((-12)-18)/10=-3

Is it that result which you need?

Answer 6

you factor it..

like if its minus 9
then the two numbers that make up 12x need to add up to become -9

like -12 and 3

Answer 7

(5x-3)(x+3)
(5x-3) >> x=3/5

(x+3) >> x=-3