Perform each division. See Examples 7 and 8. (9y2+12y-5)/(3y)

Question

Accepted Answer

Hey everyone in this problem we are asked to simplify by completely dividing the following expression were given 21 H squared plus 35 H minus nine divided by seven H. Okay so we have 21 each squared Plus 35 H - divided by seven H. Alright now we have a quadratic divided by this linear term. When we have an expression like this our denominator doesn't have any adding or subtracting. Okay we don't have a factor like seven H. Plus one. Okay we have something like this. What we can do is we can break this expression up using our common denominator. What do I mean? Well we can write 21 H squared Divided by seven H. Plus 35 H. Divided by seven H minus nine divided by seven H. The terms in the numerator are added or subtracted together and they're all divided by this common denominator. So we can break them up like this. If we did have a term like seven H. Plus one in the denominator you wouldn't want to do this. You would want to factor that numerator instead to try to cancel that factor. But when we have a situation like this where we just have seven H. In the denominator um We can break it up like this and this is gonna be the simplest way to go about this problem. All right So now we can go term by term. So starting with the first term we're gonna start with the coefficient. So we have 21 divided by seven. It's gonna give us three And then we have eight squared divided by H. Now recall when we're dividing and we have the same base. The exponents are going to subtract. Okay so we're gonna get h the exponents of the numerator to minus the exponent of the dominator. One. As we get three H. To the exponent two minus one. The next term the coefficient is 35 divided by seven. So we get five. We have a church over H. Ok you might notice that those just divide out and we're left with just the coefficient of five. You didn't notice that and you wanted to use the rule? Okay you're going to have a church. The exponent in the numerator is one minus the exponent in the non nominator is one. Okay one minus one is going to give you HD the exponent zero which gives you one. Okay so the same thing as if you realize that those H's divide out. Alright. Last term. Okay well there's nothing to be simplified here. Okay 9/7. Those are seven is a prime number. Those aren't gonna simplify, that coefficient is not going to simplify and we have over H so that can't be simplified either. So that last term is gonna stay the same. 9/7 H. Okay now the division part. The hard part is done. We're left with just simplifying by doing the subtraction here so we get three H. To the exponents two minus one gives us one. Okay so we just get three H. Plus here we have five H. To the one minus one again. That's gonna be zero. That H. The exponent zero gives us one. So we're left with just five for that middle term and then we have minus 9/7 H. Okay And so our original expression simplified is going to be three H. Plus five minus 9/7 H. And that is going to give us answer choice B. Thanks everyone for watching. I hope this video helped see you in the next one.

Perform each division. See Examples 7 and 8. (9y2+12y-5)/(3y)

Key Concepts

Polynomial Division

Simplifying Expressions

Factoring