SOLUTION: please help me solve this question {{{x^6-7x^4+12x^2}}} please explain as you solve the problem thank you

Question 321098: please help me solve this question
please explain as you solve the problem
thank you
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm assuming you want to factor.

Start with the given expression

Factor out the GCF

Now let's focus on the inner expression

------------------------------------------------------------

Looking at we can see that the first term is and the last term is where the coefficients are 1 and 12 respectively.

Now multiply the first coefficient 1 and the last coefficient 12 to get 12. Now what two numbers multiply to 12 and add to the middle coefficient -7? Let's list all of the factors of 12:

Factors of 12:
1,2,3,4,6,12

-1,-2,-3,-4,-6,-12 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 12
1*12
2*6
3*4
(-1)*(-12)
(-2)*(-6)
(-3)*(-4)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -7? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -7

First Number	Second Number	Sum
1	12	1+12=13
2	6	2+6=8
3	4	3+4=7
-1	-12	-1+(-12)=-13
-2	-6	-2+(-6)=-8
-3	-4	-3+(-4)=-7

From this list we can see that -3 and -4 add up to -7 and multiply to 12

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

------------------------------------------------------------

So our expression goes from and factors further to

Finally, we can factor to get which means that factors into

------------------

Answer:

So completely factors to

In other words,
RELATED QUESTIONS
please help me solve this question {{{25y^4-144z^2}}} please explain as you solve the... (answered by Alan3354)

please help me solve this question {{{64x^2-16x+1}}} please explain as you solve the... (answered by jim_thompson5910)

please help me solve this question {{{2x^2+10x-168}}} please explain as you solve the... (answered by jim_thompson5910)

please help me solve this question 6x�-11x+5 please explain as you solve the problem... (answered by scott8148)

Please help me solve this problem in steps y= -7x - 4 (where y= -2) Thank... (answered by checkley77)

Please help me with this problem. Thank you in advance. Please solve and show work. (answered by rfer)

please help me solve this probem = 7x -------... (answered by ikdeep)

Please help me solve this problem: x^2 - 7x I need it as soon as possible. Thank... (answered by Alan3354)

Please help me solve this problem: 9 x 10^-4 /3 x 10^-6 Thank... (answered by Fombitz)