4x² - 36x + 72 = 0?

Question

Please factor it for me because I can't seem to do it.

Answer 1

4x² - 36x + 72 = 4(x² - 9x + 18) = 4(x - 3)(x - 6).

You are asking us to FACTOR it, but by writing it out as

4x² - 36x + 72 = 0,

you seem to be really wanting us to SOLVE an equation.

That implies a little bit of mathematical confusion, which could be avoided by saying "Please solve by factoring."

The solution to 4(x - 3)(x - 6) = 0 is given by equating either of the two parentheses, in turn, to zero. That gives:

x = 3 or x = 6.

Live long and prosper.

Answer 2

When u see a 0 after the equals sign in an equation, this means u gotta solve for the variable which in this case is "x".

Now since u see that 4 is a factor of every term in the polynomial equation, so u take the 4 out as a common and then write the equation again and then finally factor it. You could also factor it directly, but it makes it a little harder. So heres how u gonna do it :

=> 4x^2 - 36x + 72 = 0
=> 4(x^2 - 9x + 18) = 0
=> 4(x - 6)(x - 3) = 0

Now u could set everything to 0, individually.

Since 3 isnt equal to 0, u cant do anything else to it.

Now get to "x". Solve for both the values of x in the parenthesis.

x - 6 = 0
x + 6 -6 = 0 + 6
x = 6

x - 3 = 0
x + 3 - 3 = 0 + 3
x = 3

So the answers are, x = 3 and x = 6.

Answer 3

sweetie u cant factor it because this equation is not for factoring, this is a "quadratic equation"! any equation that is equal to 0 is a quadratic equation which has nothing to do with factoring and u must find 2 solutions:


u need to substitute this equation into the quadratic formula:
-b +or- the square root of b^2-4(a)(c) over 2(a)! where a=4, b=-36, c=72

step1) - -36 +or- square root of -36^2 - 4(4)(72) over 2(4)
[if u have two negatives for "b" u must turn the number into a positive]

step2) 36 +or- square root of 36^2 - 4(4)(72) over 2(4)

step3) 36 +or- square root of 1296 - 1152 over 8

step4) 36 +or- square root of 144 over 8

step5) 36 +or- 12 over 8

solution#1
36 + 12 ---> 48
----------- = ------- = 6
8 ------------>8

solution#2
36 - 12 --->24
---------- = ------- = 3
8 ------------>8


both solutions for the quadratic equation are 6 and 3!
now substitute these solutions in original equation to prove its correct!
solution#1
4x^2 - 36x + 72=0
4(6)^2 - 36(6) + 72=0
4(36) - 216 +72=0
144 - 216 + 72=0
-72 + 72=0!

solution#2
4x^2 - 36x +72=0
4(3)^2 - 36(3) +72=0
4(9) - 36(3) +72=0
36 - 108 +72=0
-72 +72=0!


remember any equation set equal to "0" is quadratic. if the equation would have looked like this: factor 4x^2-36x+72, then u can factor and your answer would be:
4(x^2 - 9x +18)= 4(x-6)(x-3)

Answer 4

4x^4 - 14x^3 + 36x^2 - 84x + seventy two = 0 2x^4 - 7x^3 + 18x^2 - 42x + 36 = 0 First, enable's verify for rational roots. Divisors of 36: ±a million, ±2, ±3, ±4, ±6, ±9, ±12, ±18, ±36 Divisors of two: ±a million, ±2 So available rational roots are the divisors of 36 to boot as ±3/2 and ±9/2. Checking, we stumble on that rational roots are 3/2 and 2. ultimate roots, then, are those of (2x^4 - 7x^3 + 18x^2 - 42x + 36) / ((x - 3/2)(x - 2)) = 4x^2 + 24. 4x^2 + 24 = 0 x^2 + 6 = 0 x^2 = -6 x = ±?(-6) x = ±i?6 So the answer set is {3/2,2,i?6,-i?6}.

Answer 5

1. The answer to this after you factor it is:

(2X -12)(2X - 6) =0
I'll leave it to you to find the values of X but a hint they are in either the third or fourth quardent.:

Now to double check your answer back multiply:

4X-12
X - 6
----------
4X^2 - 12X
..........- 24X + 72
------------------------
4X^2 - 36X + 72

Way to do this thing with out putting it in a matrix or using quadratic equation is first to find all the factors of 72 i.e all the numbers when multipled together will give you 72. Also find all the factors of 4.
You have to do that first. Note I didn't say prime factors: Reason because both 72 and 4 are even nimbers:

start with the lowest and work up is the easiest:

72 divided by 1 = 72 right that is the lowest now work up.

72 divided by 2 will = 36 integer (whole number) so we use it.

36*2 =72

72 divided by 3 will = 24 so we use it.
24*3 = 72
72 divided by 4 = 18 so we use it.
18*4 = 72
72 divided by 5 = 14.4 not a whole number has fraction don't use it.

72 divided by 6 = 12 so we use it.
12*6 = 72

72 divided by 7 = 10.286 not a integer (whole number we don't use it)

72 divided by 8 = 9 so we use it.
9*8 = 72
and of course 8*9 = 72
Once you have all the factors of 72 i.e. numbers when multiplied together will give you 72 you can start factoring.

You can start anywhere you want but as an example I'll start by using 36*2 = 72

First I try:
(4X-36)(X-2)
now check.
4X-36
..X - 2
-----------
4X^2 - 36X
...........- 6X + 72
-----------------------
4X^2 - 42X RIGHT AWAY SEE THAT DOESN'T WORK
try again.
this time I try:

(X-36)(4X - 2)
NOW CHECK IT.
X - 36
4X -2
------------
4X^2 - 144X RUGHT WE SEE THAT DOES NOT WORK!
SO WE GO TO THE NEXT ONE!

(2X - 36)(2X - 2)
NOW CHECK
2X -36
2X -2
--------
4X^2 - 72X Oops that ain't going to work is it but you'll see
...........- 4X + 72
----------------------
4X^2 - 76X + 72 WRONG AGAIN !

None of the combinations of 2 and 36 worked with any of the factors of 4: So we go to the next set. and try all combinations of them if they don't work go to the next set.

In this case had to keep trying unitl got to the combinations of the sets of 6 and 12 and the factors of 4.

Started off with:
(4X - 6)(X - 12)
CHECKED
4X - 6
X - 12
----------
4X^2 - 6X
..........-48X + 72
---------------------------
4X^2 - 54X + 72 WELL THAT DIDN'T WORK DID IT SO WE GO TO THE NEXT SETS.

(2X - 12)(2X - 6)
NOW CHECK!
2X - 12
2X -6
----------
4X^2 - 24X
..........- 12x + 72
-----------------------
4^2 - 36X + 72 Hay that works! but what about the next sets?

(4X - 12)( X - 6)
NOW CHECK!
4X - 12
X -6
---------
4X^2 -12X
..........- 24X +72
----------------------
4X^2 -36X + 72 Hay it works as well but do you see anything wrong with it? Is all factors reduced as low as they will go? What a 4? As seen above it can be reduced to the factors 2*2 right
That means even though (4X - 12)(X - 6) Has not been factored down as low as it will go.
SO THE CORRET ANSWER IS:
(2X -12)(2X - 6) =0

That's the way you work it when factoring: But it takes a lot of practice to get good at it.
First thing you have to know your multiplication tables real good as well as your addition and subtraction tables real good.
Hope that helps show you how to factor and understand factoring a little better.

Answer 6

4x^2 - 36x + 72 = 0 (divide both sides by 4)
x^2 - 9x + 18 = 0
(x - 6)(x - 3) = 0

So, either x-6=0 or x-3=0
x=6 or x=3

Answer 7

I'd remove the 4 first and make it look like this:

4(x^2 - 9x + 18) = 0

Then, factor it:
4(x - 3)(x - 6) = 0

Answer 8

factor out a 4:

4*(x^2-9x+18)

then factor the ()'s:

(x-6)(x-3)

ANS: 4*(x-6)(x-3) = 0

x = 6, 3

Answer 9

4[(x-6)(x-3)]

Answer 10

4(x^2-9x+18)= 4(x-3)(x-6)