Factor Completely
6^8+12x^6-24x^4+30x^2
I got
6x^2(x^6+2x^4-4^2+5)
Correct?
Yes, you have a typo on the -4x^2 term
Thank you. I am not feeling 100 percent confident in this topic, so you might see a few more, i do appreciate the help!
No, your factoring is incorrect. Let's go through the factoring process step by step.
The given expression is:
6^8 + 12x^6 - 24x^4 + 30x^2
First, let's try to find a common factor among all the terms. The greatest common factor (GCF) among all the terms is 6x^2:
6x^2(6^6 + 2x^4 - 4x^2 + 5)
Now, let's focus on factoring the expression inside the parentheses: 6^6 + 2x^4 - 4x^2 + 5.
Unfortunately, this expression cannot be factored any further using integer coefficients. Therefore, the factored form of the given expression is:
6x^2(6^6 + 2x^4 - 4x^2 + 5)
Note: In cases where the expression inside the parentheses can be factored using integer coefficients, you can further factor it by using techniques like factoring by grouping, difference of squares, or trinomial factoring.