In Exercises 45–66, divide and, if possible, simplify.
_______
³√...

Question

In Exercises 45–66, divide and, if possible, simplify.
_______
³√x²+7x+12
³√x+3

Accepted Answer

Welcome back. I am so glad you're here. We are asked for the following expression, perform division and further simplify if possible. The expression we're given is in the numerator, we're taking the Q dr of H squared plus 15 H plus 54. And that's divided by our denominator, which is the cube of H plus six. Our answer choices are answer choice. A, the cube of H plus nine. Answer choice B the QT of H plus eight, answer Tracy, the cube of H plus seven and answer choice D the cubed of H plus six. All right, we recall from previous lessons that when we're taking a root of both our numerator and our denominator and it's the same rut we can take that root of. In this case, it's the cubed rut of the entire fraction. So our numerator would be H squared plus H plus 54 our denominator is H plus six. So now it's just a matter of, can we divide H squared plus 15 H plus by H plus six? And we need to determine that by figuring out if there are any factors that cancel out in our numerator in our denominator. So we want to factor our numerator, the denominator is already as factored as it gets, but H squared plus 15 H plus that could possibly be factored. So we'll do the reverse of the foil process to see if it can. First, we ask ourselves what multiplied by what gives us H squared. That's going to be H multiplied by H those are our firsts. Then we look at our lasts, we ask ourselves what multiplied by what equals a positive 54. And at the same time, those as our outsides And insights need to add up to a positive 15 h. So what two numbers when multiplied equal, positive 54 and when added equal positive 15, that's going to be a positive six and a positive nine. So we have this factored, we're taking the cube dr of in our numerator instead of H squared plus 15 H plus 54. We have the factored Each plus six multiplied by H plus nine. And our denominator is still H plus six. But now we see that there is an H plus six factor in both our numerator and our denominator and those can cancel out. So now all that's left is the cube dr of H plus nine. And that's as simplified as that one gets. We look at our answer choices and this matches with answer choice. A well done. We'll catch you on the next one.

In Exercises 45–66, divide and, if possible, simplify. _______ ³√x²+7x+12 ³√x+3

Key Concepts

Radical Expressions

Factoring Polynomials

Simplifying Rational Expressions

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