I’m going to divide these polynomials using long division. The first thing I’m going to do is write my divisor out here x minus 4, then this things what we call the dividends this whole big enchilada goes underneath 2x to the third minus 13x² plus 17x plus 12. That whole thing goes under the division sign.
What I’m going to be doing is thinking about how many times does x multiply into 2x to the third. It’s kind of like un-distributing. X times what gives me 2x to the third? Well I know I’m going to need a 2 and I’m also going to need 2 more Xs so that’s going to be 2x². I’m going to write it here on top of my x squared to line everything out. You’ll see why later.
Okay, next thing I’m going to do with the process of division is you do this guy times that guy and write your answer here and then subtract them so here we go. 2x² times x is 2x to the third and that’s good because that’s the way I planned it. Then 2x²times -4 will be -8x². The next thing I’m going to do is subtract this from that.
Be really, really careful that both of these terms are going to get subtracted. Don’t lose this minus and negative that becomes important. So 2x to the third take away 2x to the third is 0x to thirds. 13x² take away negative is the same thing as adding 8x² so I’ll have -5x² there. Just like your old school long division, next thing you do is bring down this next term and I’m going to repeat the process. How many times does x go into -5x²? Well I know I need the -5 and I also need one more x lining it up on top of my regular x terms here will help keep my work organized. -5x times x is -5x², -5x times -4x will be +20x and then again be really careful that you subtract this whole thing.
If you make a mistake in your homework problems, my guess is it’s in this step. You forgot to subtract both of these terms. It’s really important. 5x² minus, minus 5x² will be 0x² it's good 17x take away 20x will be -3x, bring down your next term. I’m almost done. X times what gives me -3x, it’s going to be -3 make sure I’m being careful with the negative signs. -3 times -4 is +12 sweet. When I subtract that I end up with a remainder of 0.
So that tells me this is my final answer. This third degree 4 term polynomial divided by that guy gives me that quotient. That’s how you do this long division using polynomials. To check your work I'm not going to show you the whole process I just want to show you how, to check your work you would do this times that and this should be your answer. This thing is called the divisor, divisor times the quotient should give you the dividend. So if you wanted to check your work, you would go through and do a whole bunch of distributing this times that gives you that answer.
So guys the last thing I want to leave you with before you try these problems is to please, please, please be careful with distributing this negative. If you’re making errors in your homework again it’s probably because you forgot to subtract both of these terms.
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