Hey I need help factoring 5x^4-180x^2. I'm used to factoring with three numbers, and not two. How would you do just two like this? Thanks
first of all I see a common factor of 5x^2
so
5x^4-180x^2
= 5x^2(x^2 - 36)
Now isn't that a difference of squares???
To factor the expression 5x^4 - 180x^2, we can first look for a common factor. In this case, both terms have a common factor of 5x^2. So we can factor it out as follows:
5x^2(x^2 - 36)
Now we have a quadratic expression within the parentheses (x^2 - 36), which we can further factor. Looking at this expression, we notice that it is the difference of squares, since 36 can be expressed as 6^2.
So, we can factor it as:
5x^2(x + 6)(x - 6)
Thus, the factored form of 5x^4 - 180x^2 is 5x^2(x + 6)(x - 6).
To summarize the factoring process:
1. Identify if there is any common factor among the terms.
2. Factor out the common factor.
3. Check if there are any additional factorization opportunities, such as a difference of squares, a perfect square trinomial, or grouping.
4. Continue factoring until no further factorization is possible.