hey i need some help?

Question

Hey what i need help with factoring...?
hey what would be the answer to y4+y2-2
all the numbers after the y's are variables except the last 2 thx for the help

Answer 1

What factors of -2 add to +1?
2 times -1 is -2
and 2 plus -1 is +1.
y^4 + y^2 - 2
= (y^2 -1)(y^2 +2)
y^2 - 1 is a difference of squares, so you can factor that into
(y-1)(y+1)
Answer: (y-1)(y+1)(y^2 +2)

Answer 2

I think you mean the numbers are exponents, not variables

y^4 + y^2-2 = 0

Here's the trick: regroup the numbers to make the difference of two squares twice:

y^4 -1 + y^2-1 = 0

y^4-1 = [(y^2)^2 - 1^2]
= (y^2 -1)(y^2 +1)


Substituting these back into the original equation:

(y^2-1)(y^2+1) + (y^2-1) = 0

Taking out the common factor:

(y^2-1) [(y^2+1) + 1] = 0

Either y^2-1 = 0 => (y+1) (y-1) = 0
so y = +1 or y = -1

Or y^2 +1 +1 = 0

y^2 + 2 = 0

y^2 = -2

y = + 2i or y = -2i

So your four possible solutions are

y = { 1, -1, 2i, -2i}

Answer 3

substitute t= y^4 to simplify notation
you get y^4 + y^2 - 2 is t ^2 + t - 2

t^2 + t -2 = (t -1)^2 +3t -3 <-- adding stuff to balance sides
= (t -1)^2 +3(t-1) <-- extract common component (t -1)
= (t -1) (t -1 + 3)
= (t -1) (t +2)

and substitute t back with y^2 to get
y^4 + y^2 - 2 = (y^2)^2 + y^2 - 2 = (y^2 - 1) (y^2 +2)

If you are interested why I considered (t-1)^2 above here is the explanation: t^2+t-2 looks very similar to a solution of
(t +/- 1)^2, therefore I used it as a base. Because it is less than the original expression I had to add something (in this case 3t -3) to balance both sides.

Answer 4

y^4 + y^2 - 2

The first thing you should notice is that y^4 = y^2 * y^2

Also, the last term is negative. In order to get that, you will need to have a positive multiplied by a negative.

(y^2 + ? )*(y^2 - ? )

Now we need to figure out the last terms. When you multiply them together, they must equal (-2) and when you add them they should equal 1.

2 and (-1) do that, so:

(y^2 + 2 )*(y^2 - 1 )

Also notice that (y^2 - 1 ) is a difference of squares, which can be factored as:

(y - 1)*(y + 1)

So your final answer is:

(y^2 + 2 )*(y - 1)*(y + 1)

Answer 5

Factors of y^4 + y^2 - 2 are (y^2 + 2) and (y^2 - 1). Do you know how to do it stepwise?

Hope this helps!

Answer 6

y^4+y^2-2...Factor the first two.
y^2(y^2+1)-2...i think thats all you can do

Answer 7

you're missing an =