Factor completely, or state that the polynomial is prime. 3x^4-12...

Question

Factor completely, or state that the polynomial is prime. 3x^4-12x^2

Accepted Answer

Hi there. So for this problem says faculty given polynomial completely or categorize the polynomial to be prime. If it can't be fact arised furthermore serve this problem, I'm going to rewrite it. First of all you have seven X. The sixth minus 28 X. The fourth one thing I can check first is if I can factor up my coefficients. So is there a common factor between seven and 28? The way I do this is I'm gonna divide my larger coefficient over my smaller coefficient. So so we have 20/7. Is this going to be a whole number? You know 20/7 is four. So yes, this is a whole number. So I know I now know that I can fetch up a seven out of both expressions. So if we go back to our problem In fact is seven out of both of them. What I do that And be left with an X. to the 6th here and Taking a seven of 28 We left with a four X to the four. I'm gonna try and factor out our experts. So do we have An excellent. That'd be taken out of X to the 6th and X to the four. That's the question. So similar to the coefficients. I'm gonna divide by X. One, X. 2 to 6. The larger one over the smaller one X to the fourth. And we'll see if we can do this now we don't want to get a negative X on it because then it's not simplified anymore. Some We have X the 6th over the four. If you call for your book Korea listen when you divide exponents we're going to subtract the degrees of each expression. Some in this case I have X. Six since we're defined by X to the fourth I'm gonna subtract four Now we'll go ahead and simplify this. Exodus 6 -4 that is X squared. So we do have a positive exponents which means this will work to factor out X to the four. So if we go back to our problem We have seven. We factor out an X to the four now and then we'll go ahead and write what's left X. The sixth background X to the four. We found that over here that is X squared now we're factoring on X to the four. From an X to the fore. That will just be one. Or just leave that as -4. So that leaves us with seven X to the fourth times X squared minus four. And that's our answer. His answer is C. Okay I hope to help you solve the problem. Thank you for watching. Goodbye

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