if any one have guts then , factorize x^4 + 16x -12 =0?

Question

it came in 5th grade examination

Answer 1

LET Y=X^4 + 16X -12 =0
=>X^4 + 4X^2 - 4X^2 -12 + 16X=0......adding and subtracting 4x^2
Because we need to convert 4 th power into a square.

=>(X^4 + 4X^2 + 4 - 4) - (4X^2 + 12 - 16X)=0........add, sub 4 in 1st bracket
=>(X^4 + 4X^2 + 4) - (4X^2 + 16 - 16X) = 0
=>(X^2 + 2)^2 - 4(X^2 + 4 - 4X)=0
=>(X^2 + 2)^2 - 4(X - 2)^2=0
THIS IS OF FORM (A^2 - B^2)=(A+B)(A-B)
=>(X^2 + 2 +2(X-2))(X^2 + 2 - 2(X-2))=0
=>(X^2 + 2X - 2)(X^2 - 2X + 6)=0

p.s. isn't that difficult!

Answer 2

the ideal format would desire to be (?x +/- n)(?x +/- n) ? & n are the two numbers. each and all of the values in the 1st set of brackets is extra effective by employing each value in the 2nd set of brackets. this might supply: ?x^2 +/- ?nx +/- n?x +/- nn Like values are then further. the place the n? or ?n looks, it only means that the two numbers that they characterize are extra effective. n?x or ?nx means the two numbers are extra effective yet have the x following them. The final huge style on the equation which you're asked to factorize, is produced by employing multiplying the two n values. hence +sixteen. So which 2 numbers produce +sixteen? 0 & +sixteen, +2 & +8, +4 & +4. besides the fact that, by way of fact the middle value is a adverse, this means that the two between the n values are adverse. by way of fact including 2 adverse values produces a adverse, at the same time as multiplying 2 adverse values will supply a effective! this is the only way that the middle and end numbers would be the two plus and minus (i think of!) So 0 & -sixteen, -2 & -8, -4 & -4 will additionally supply a +sixteen very final value. The -16x value is calculated by employing including the ?nx value and the n?x value. they're, in spite of everything, the two x to the skill a million values. while the two ?x values are extra effective, you get an x to the skill 2 result. This value comes first in the equation you're asked to factorize. So, we would desire to locate 2 numbers that as quickly as extra effective mutually will supply +sixteen and while further mutually will supply -sixteen. i might advise sixteen & 0. Or 0 & sixteen. So, (4x - sixteen)(x - 0) Will supply 4x^2 - 16x + sixteen besides the fact that, I actual have concluded that diverse areas of the international try this element otherwise; so this is probably not what you're in seek of for!

Answer 3

x^4+16x = 12
(x^2)^2+((4)^2).x = 12
it is in the form of a^2+b^2 that = (a+b)^2 - 2ab
where a=x^2 and b=4
(x+4)^2-8x.x = 12
(x+4)^2-8x^2 = 12
(x+4)^2-(x)^2.8 = 12 a^2-b^2 = (a+b)(a-b)
(x+4+x)(x+4-x).8 = 12
(2x+4)(4).8 = 12
8x+16.8=12
8x+128 = 12
8x = 12 - 128
8x = -116
x = -116/8
x = -14.5

Answer 4

^4+16x = 12
(x^2)^2+((4)^2).x = 12
where a=x^2 and b=4
(x+4)^2-8x.x = 12
(x+4)^2-8x^2 = 12
(x+4)^2-(x)^2.8 = 12 a^2-b^2 = (a+b)(a-b)
(x+4+x)(x+4-x).8 = 12
(2x+4)(4).8 = 12
8x+16.8=12
8x+128 = 12
8x = 12 - 128
8x = -116
x = -116/8
x = -14.5

Answer 5

x^4 + 16x - 12 = (x^2 - 2x + 6)(x^2 + 2x - 2)

I used www.quickmath.com

Answer 6

Easy

Answer 7

i believe you are missing a square on the second term. You can't factor that and get a singular x on the 2nd term.

Answer 8

I have finally figure out....
It take's brain than guts to solve this.

Answer 9

smart 5th grader, thats all i have to say. i cant figure it out and math is my fave.