Factorize the following :
x4-x2-6
HELP!!!!!!
Do you mean,
x^4 - x^2 - 6
This was answered the first time you posted it. I pasted the answer here for you.
(x^2 - 3)(x^2 + 2)
HEY CAT :) First, to find it, you have to find the factors of six that could equal -1, because -x is the same thing as -1. So the factors would be -3 and +2, right? So in brackets, it would be: (x^2-3) (x^2+2) :) HOPE I HELPED!
omg tilla!! :D you totally helped. thankiess!!
To factorize the quadratic expression, x^4 - x^2 - 6, we can use a method called grouping.
Step 1: Notice that our equation has two terms, so we want to split the middle term (-x^2) into two terms that can be grouped.
Step 2: To factorize the quadratic expression, consider the two terms x^4 and -6 separately and factorize them individually.
For x^4, notice that it is a perfect square because x^2 * x^2 = x^4. So, x^4 can be written as (x^2)^2.
For -6, we need to find two numbers that multiply to give -6 and add up to give -1 (the coefficient of x^2). The numbers -3 and 2 fulfill these conditions since -3 * 2 = -6 and -3 + 2 = -1.
Step 3: Now, rewrite the middle term (-x^2) by replacing -1x^2 with -3x^2 + 2x^2.
The expression x^4 - x^2 - 6 becomes:
x^4 - 3x^2 + 2x^2 - 6
Step 4: Group the terms:
(x^4 - 3x^2) + (2x^2 - 6)
Step 5: Factor out the common terms from each group:
x^2(x^2 - 3) + 2(x^2 - 3)
Step 6: Notice that the terms (x^2 - 3) are common in both groups, so we can factor out (x^2 - 3) from both terms:
(x^2 - 3)(x^2 + 2)
Therefore, the factorized form of the quadratic expression x^4 - x^2 - 6 is (x^2 - 3)(x^2 + 2).