factor 80x5th power -360x3rd power + 405x
80x^5 - 360x^3 + 405x
5x(80x^4 - 72x^2 + 81)
in parentheses is just a quadratic in x^2, so
x^2 = (9 ± 16i)/20
Now, just take the square roots of those complex numbers to get your other factors :-)
Sure there's no typo there?
Oops 80/5 = 16. Makes a big difference
5x(16x^4 - 72x^2 + 81)
5x(4x^2 - 9)^2
5x(2x-3)(2x-3)(2x+3)(2x+3)
54x3y
sorry that answer was wrong tis is the right one 3x(43+82/3)*(879/615=y78)
To factor the expression 80x^5 - 360x^3 + 405x, we can look for the greatest common factor (GCF) and then use the factoring techniques like factoring by grouping.
Step 1: Find the GCF
The common factor among the terms is x, so we can factor out x from each term:
x(80x^4 - 360x^2 + 405)
Step 2: Factor the expression in parentheses
Now we focus on factoring the expression inside the parentheses: 80x^4 - 360x^2 + 405.
We can first look for a common factor among all the terms, but in this case, there is no common factor other than 1.
Next, we can try to see if it is a perfect square trinomial. However, if we square any term, such as (4x)^2, we get 16x^2, which is not equal to 80x^4. So it is not a perfect square trinomial.
Now, we move on to factoring by grouping:
Step 3: Factoring by grouping
Let's group the terms and factor them separately:
80x^4 - 360x^2 + 405
= (80x^4 - 160x^2) + (-200x^2 + 405)
Now, let's factor out the common factors from each group:
= 80x^2(x^2 - 2) - 200(x^2 - 2)
Notice that we have a common binomial factor in both terms, namely (x^2 - 2). Let's factor it out:
= (x^2 - 2)(80x^2 - 200)
Step 4: Simplify further if possible
If desired, we can simplify this expression further:
= (x^2 - 2)(4x^2 - 10)
= (x^2 - 2)(2x^2 - 5)
So, the factored form of the expression 80x^5 - 360x^3 + 405x is (x^2 - 2)(2x^2 - 5).