x^4 -3x^2 - 4
how to factor this? Thanks
(x^2 - 4)(x^2 + 1)
To factor the expression x^4 - 3x^2 - 4, we can follow these steps:
Step 1: Check for Common Factors
In this case, there are no common factors among the terms x^4, -3x^2, and -4, so we move on to the next step.
Step 2: Identify Potential Factoring Techniques
Since the expression has the form of a quadratic trinomial (x^2) with a coefficient of 1 in front of the x^2 term, we can apply factoring techniques for quadratic expressions.
Step 3: Factor the Quadratic Expression
We can rewrite the expression as follows:
x^4 - 3x^2 - 4 = (x^2)^2 - 3x^2 - 4
Now, let's try to factor it by grouping:
(x^2 - 4)(x^2 + 1)
We can further check if this factored form is correct by expanding it:
(x^2 - 4)(x^2 + 1) = x^4 + x^2 - 4x^2 - 4 = x^4 - 3x^2 - 4
So, the factored form of the expression x^4 - 3x^2 - 4 is (x^2 - 4)(x^2 + 1).