Perform each division. See Examples 9 and 10. (x^2+11x+16)/(x+8)

Question

Accepted Answer

Hello, today, we're gonna be simplifying the given quantity by using long division. So what we are given is V squared plus three V plus 25. And we're going to be dividing this quantity by V plus five. Now, before we set up our long division, you always want to check to make sure whether you're missing any terms in the numerator or not here, we're not missing any terms. So we can go ahead and set up the long division right away. So what we have is V squared plus three V plus 25 we're gonna be dividing this quantity by V plus five. Now, in order to start this, you want to go ahead and ask yourself what is a number that I can multiply V plus five by to get V as close as possible to V squared while I can multiply this quantity by V as V plus five times V while you're going to go ahead and distribute V into V plus five, and that's going to give us V squared plus five V, you're gonna put this quantity underneath which is going to be again, V squared plus five V. But you want to go ahead and be careful here because we want to subtract this quantity from the entire numerator. So since we're subtracting V squared plus five V, we're going to need to distribute the negative sign into V squared plus five V and that's going to change the signs of this quantity. So what we now have is negative V squared minus five V and now we can continue with the simplification. So V squared minus V squared is going to cancel itself out and positive three V minus five V is going to give us negative two V. We bring down the next term which is going to be 25 we're going to repeat this process now again, what's a number that we can multiply V plus five by to get V as close as possible to negative two V. Well, you can multiply it by negative two as V plus five, multiplied by negative two. You're going to distribute negative tune to V plus five. That's going to give us negative two V minus 10. So again, you put this quantity underneath negative two V minus 10. And again, we want to subtract this quantity. So we're going to need to distribute the negative sign into negative two V minus 10. Doing this is going to change our signs. And what we now have is positive two v plus and so negative two V plus two V is going to cancel itself out. And 25 plus 10 is going to give us positive 35 this is going to be our remainder. So let's go ahead and put the quotient together what we calculated was V minus two. And we're going to need to include the remainder into this quantity. The remainder is a positive value. So we're gonna be adding the remainder to V minus two and we're gonna represented as a fraction where the actual value of the remainder is gonna go in the numerator. So 35 goes in the numerator and we're gonna keep the original denominator given to us, which is going to be V plus five. And this is going to be the simplified version of the given quantity using long division. And with that being said, the answer to this problem is going to be a, so I hope this video helps you in understanding how to use long division. And I'll go ahead and see you all in the next video.

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Perform each division. See Examples 9 and 10. (x^2+11x+16)/(x+8)

Dividing Polynomials practice set