Perform each division. See Examples 7 and 8. (-4x^7-14x^6+10x^4-1...

Question

Perform each division. See Examples 7 and 8. (-4x^7-14x^6+10x^4-14x^2)/(-2x^2)

Accepted Answer

Hey everyone welcome back in this problem we are asked to simplify by completely dividing the following expression. And the expression were given is negative 55 H squared minus 22 H. To the exponent nine plus 88 H. The exponents six minus 44 H cubed divided by negative 11 H cubed. So let's just rewrite the expression were given each to the 12 minus 22. Each to the nine plus 88 H. To the six. And just be careful when you're rewriting copying over the expression that you're not making any mistakes with the exponents or anything like that. Can be easy to mix up one of the exponents when you're writing it out and then the answer will be wrong unfortunately. Alright so that's the expression that we're trying to simplify. Well you'll notice is that we have just this one term in the denominator. We don't have anything added subtracted and we have all of these terms added and subtracted in the numerator. So what we can do is we can break this up into four separate pieces. Okay and then we only have to deal with one at a time. It's gonna be a little bit simpler. So we have negative 55. HD exponent 12 divided by negative 11. HD exponent three minus 22. HD exponent nine over negative 11 H. To the exponent three plus A. D. H. D. Experiment six divided by negative 11. HD experiment three and finally negative 44 H cubed divided by negative 11 H cubed. Okay so you'll see we have this negative 11 H Cubans are a common denominator and so we can break this into four terms using that common denominator. Alright now one term at a time we have negative K. Start with just the coefficient negative 55 divided by negative 11 is going to give us positive five. And then we have a church to the exponent 12 divided by H. The exponent three when we have the same base and we divide the exponents are gonna be subtracted so we're gonna end up with a church. Okay? And then we're gonna take the exponent from the numerator 12 and subtract the exponents from the denominator three. So we get five H. To the exponent 12 minus three for that first term. Alright moving to the second term, we have negative 22/-11. It's going to be positive too. And then we have a church to the exponent nine divided by H. To the exponent three. So we get H. To the nine minus three. Next term 88 divided by -11. That's gonna be -8. Okay and then our H. We have H. Two. The experiment six divided by H. To the experiment three. So we get H. To the six minus three In our final term -44 divided by -11 gives us positive four. We get h cubed divided by H cube. So we get H. T. Exponent three minus three. Alright so now we just need to simplify and do this division. The hard part is done we just have one last step. So we have five H. K. 12 minus three is going to be nine Plus two. H 9 -3 is going to be six -8. H 6 -3 gives us three. And finally plus four and we have a church to the exponent three minus three. That's gonna be a church to the exponent zero which gives us one. Okay so we just have the constant four there. And so our expression original expression simplified is going to be given by five H. To the exponent nine plus two. H. To the exponent six minus eight. H cubed plus four which is going to be answer. D. Thanks everyone for watching. I hope this video helped see you in the next one.

Perform each division. See Examples 7 and 8. (-4x^7-14x^6+10x^4-14x^2)/(-2x^2)

Key Concepts

Polynomial Division

Simplifying Expressions

Negative Exponents