Perform each division. See Examples 7 and 8. (15m^3+25m^2+30m)/(5...

Question

Perform each division. See Examples 7 and 8. (15m^3+25m^2+30m)/(5m^3)

Accepted Answer

Hey everyone in this problem we are asked to simplify by completely dividing the following expression Were given 21 H cubed plus 35 H squared plus 84 H divided by seven H. Cubed. Okay so we're rewriting that expression 21 H cubed plus 35 H squared plus 84. H. Divided by seven H. Cute. All right now we're giving an expression like this and the denominator we just have this seven H. Cubed term. Okay we have no addition or subtracting or subtraction. Um so we don't have any factors like H. Plus two or anything like that in the denominator. Um In our terms in the numerator are separated by addition. So what we can do is we can break this expression into three parts. We can write this S. 21 H cubed divided by seven H. Cubed plus 35 H squared divided by seven H. Cubed plus 84 H. Divided by seven H. Cubed. Okay. Seven HQ bizarre. Common denominator. And these terms are added together so we can break them up like this. Okay now we can work term by term. So we have the first term 21 H cubed divided by seven H. Cubed. Okay so let's start with the coefficients 21 divided by seven is gonna give us three. You might notice right off the bat that H cubed divided by H cube. Okay that's gonna cancel. We're gonna let me left with just one. Okay if you didn't notice that recall that the rule for dividing If we have the same base. The exponents get subtracted so we'll get three h. To the exponent 3 -3. Okay three minus three is going to be zero. Hc exponent zero is going to be one. Okay so we get back to that one. Just like if you had noticed that those divided right off the bat. Alright next we have 35 K. In terms of coefficient 35 divided by seven is gonna give us a coefficient of five And then we have a church and we're gonna do the subtraction in the numerator we have the exponent to the denominator. We have the exponent three. So we get 2 -3. Okay you always take the exponents of the numerator minus the exponent of the denominator. Okay you don't want to mix up that order. Alright and then this last term we have 84 divided by seven. That gives us a coefficient of 12 and then we have a church divided by H. Cube. So we're gonna get H to the exponent 1 -3. Alright so the hard part is done. We've done the division. What we need to do now is just simplify these exponents by doing the subtraction. So here again three H. To the exponent three minus three. That's gonna be ht the exponent zero which gives us one. So we get three. Okay we get plus five hc exponent two minus three is going to be a church to the negative one and then 12 H. To the exponent one minus three is going to be a church to the exponents negative two. All right now we want to rewrite this. If we look at our answer choices, okay? We see that these have been rewritten as fractions instead of these negative exponents. Okay, so let's recall that if we have a negative negative exponents we can write it in the denominator um with a positive exponent. So we can write this as three Plus five over HK H to the exponent one. And then we get 12 over h squared. And so the simplified version of that original expression is going to be three plus five over H plus 12 over H squared which is going to be answer. A thanks everyone for watching. I hope this video helped see you in the next one.

Perform each division. See Examples 7 and 8. (15m^3+25m^2+30m)/(5m^3)

Key Concepts

Polynomial Division

Simplifying Expressions

Coefficients and Exponents