How do you factor these out?

Question

16^2+24x+9=0
9x^2-18x+9=0

Answer 1

For the first one: at least one x factor is going to have a coefficient other than 1. First, list the possible factors (neglect fractions):
for 16: 1/16, 2/8, 4/4 - and the opposite pairs of -1/-16, etc.
Now, think about the constant of 9. Find factors for nine: 1/9, 3/3 - and their opposites of -1/-9 and -3/-3

Now it's a matter of putting these pairs together in a way that will give you 24x. Assume everything is positive for now (since all your coefficients in the quadratic are positive, that means that your factors are either all positive or all negative).
Try the combinations. You'll find that 4/4 and 3/3 work:
(4x + 3)(4x +3) = 16x^2 + 24x + 9

The second one is trickier. Again, we have the same list of numbers from which to choose. However, the negative coefficient on -18x complicates things.

What I would do on this one is just divide everything by 9. Way easier to solve it then: x^2 - 2x + 1 = 0
Can you solve it? You should get (x - 1)(x - 1) = 0

Of course, that gives you the solution to the quadratic, not the factoring of the original quadratic. To get back to the original and how to factor it, just multiply the (x - 1)(x - 1) factors by 9. That undoes the step of dividing the original quadratic by 9:
9* (x - 1)(x - 1) = 0
(9x - 9)(x -1) = 0
Note that I distributed the 9 factor to just one of the (x - 1) factors. Otherwise you'd be multiplying by 9*9 = 81.
If you want, check the above factoring. You'll find that
(9x - 9)(x - 1) = 9x^2 - 18x + 9

Answer 2

well based on how you wrote it:
24x+9+256=0
24x+265=0
24x=-265
x= -265/24

9(x^2 - 2x + 1)=0
9(x-1)(x-1)=0
so x=1

and in the event that you may have written the first problem incorrect
and you ment 16x^2 + 24x + 9 = 0
divide by 16 x^2 + (24/16)x + (9/16) = 0
reduce (24/16)x to (3/2)x
and complete the square
(x + 3/4)(x + 3/4)=0

so that x = -(3/4)

Answer 3

2. Factor out a common factor first (if possible):
9 (x^2 -2x +1)
Because it is x^2 you need to multiply x time x.
Then you need to find the factors of 1.
Because 1 is the only factor of 1, it must be
(x +or- 1)(x +or- 1).
Because 1 is positive, both 1's must be the same sign.
Because 2 is negative, they must be negative signs.
Therefore the answer is:
9 (x- 1)(x- 1)

Then you can FOIL to check it.
F= "first"
Multiply by the First number in each quantity.
X x X= X^2
O="outer"
Multiply by the Outer number in each quantity.
-1 x X= -1X
I="inner"
Multiply by the Inner number in each quantity.
-1 x X= -1X
L="last"
Multiply by the Last number in each quantity.
1 x 1= 1

x^2-1x-1x+1=
x^2-2x+1
Then multiply it by the common factor that was taken out.
9(x^2-2x+1)=

9x^2-18x+9 <<

#1 work the same way. It was just easier to do this one.

Answer 4

The question is not clear--Put X $ y in the equation to solve it.

Answer 5

(4x+3)(4x+3)=0
x=-3/4

(3x-3)(3x-3)=0
x=1