All right we’re on problem number nine: A list of the first next the next view, I don’t think I have to copy and paste this problem like I can just write it so they—looks like a little bit of algebraic long division problem nine.
They want us to divide 2X plus 7 into—it’s pretty long so get some space—2X to the forth plus twenty one X to the third plus thirty five X squared minus thirty seven X plus forty six. This might look daunting but once you start it it’s not so bad. So like any long division you kinda look at the biggest place and the — largest degree place at least on these panel in the middle is 2x place and that is what we worked with so we say how many time does 2X go into 2X to the forth? Was it the 2 goes into the 2 one time and X goes into the X to the forth, X to third time right? What’s X to the forth divided by X? It’s X to third, so we said goes into it X to the third times and if we’re right when we multiply we should get 2X to the forth so X to the third times 2X is 2X to the forth and then X third times 7 is plus 7X to the third right?
If this was like a—you know—some other—if this was—well we will worry about it when we get to it. But you’d—you’d want to put under the appropriate place in this number but it just happen to be that X to the third was an extra one. Now you subtract just like you do regular long division. These cancel out, twenty one minus 7 is 14X to the third and then you could bring down all of these but we can worry about that on the second. So how many times does 2X go into 14X to the third with 2 goes into 14 seven times plus seven and X goes into X to the third X squared times and for right we re multiply it should work out so 7X squared times 2X is equal to 14X to third like we thought it should. 7X squared times 7 is what? That’s plus forty nine —forty nine X squared and now we subtract 14X to the third minus 14X to the third, that’s zero. Now we have thirty five we could bring this down, just to makes it easier. 35X squared—35X squared minus forty nine X squared, let’s see, so it minus 14 right? Forty nine minus thirty five right so that’s minus 14X squared and then 2X goes into minus 14X squared so 2 goes in the minus 14 minus 7 times and then X goes into X squared X times, when you multiply minus 7X times 2X so you get minus 7 times 2 is minus 14. X times X is X squared, of course you have to multiply time both terms right?
We’re multiplying times these whole expression minus 7X times 7 is minus forty nine X—minus forty nine X, now we’re ready to subtract again and I’m running out of space. This cancel out, we could bring this minus thirty seven X down so minus thirty seven X—remember we’re subtracting this right? We could almost say, we could almost add the negative right? Let’s make the negative, so if this is minus thirty seven X minus forty nine minus same thing is minus thirty seven X plus forty nine X. I added—I made both of those positive just to simplify it on my brain —I didn’t want to go down that much. Okay so this is equal to—this cancel out and then this is equal to twelve X and 2X plus 7 goes into twelve X, when I will see 2 goes into twelve 6 times goes into X one time so then this is equal to plus six. Six times 2X plus 7, 6 times 2X I know you can’t see it is twelve X and then 6 times the seven—6 time seven is forty two—forty two—you have forty six up there—I should have written it smaller so you see it’s forty six and now we’re ready to subtract again.
Twelve X minus twelve X is zero, forty six minus forty two is four so have a remainder of four so let’s see—our answer is—all of this with the remainder four so all of that plus the remainder over what we’re done—use it to divide it to. 2X plus seven so that’s—our answer, let’s see what choice it is. It’s X to the third plus seven X squared minus seven X plus 6 plus 4 over 2X plus seven. We just took our remainder and take whatever this is—that’s also there. So that is choice—let’s see X to the third plus seven X squared minus seven X plus six plus four over 2X plus seven—that actually choice D is our answer. I was just reading —I was just reading choice A. I should have shown you that on the —so choice D is our answer. Next question problem number ten.
Now I took out more space than I’ve expected. Problem number ten. Which problem may we represent? So they want us to multiply, this is how they write it, 3X squared plus X minus 4 times 2X minus 5.I find this —you know multiply this way I would multiply any number so I would—I’ll rewrite this 3X squared plus X minus 4 times and I’ve put those same degree under the same degree times 2X minus 5. And now let’s take the zeroth degree place, I guess you could view that way minus 5 times minus 4 is plus twenty, minus 5 times X is minus 5X, minus 5 times 3X squared is minus fifteen X squared—minus fifteen X squared, 2X times minus 4 is minus 8X, I’ll put it in this place because that’s our X space minus 8X, 2X times X is 2X squared—2X squared and then I should have had all of this actually I think I can do that—let me see if can move all of this to the right— the magic of computers. I can move it all to the right although after I can color back that in—let’s see if I can color that. Look at that.
All right back in business, alright so I did 2X times minus 4 is minus 8X, 2X times X is 2X squared, 2X times 3X squared is 6X to the third—6X to the third, this is a plus now just add up everything. Add up everything so we get 6X to the third minus fifteen plus 2 minus thirteen X squared minus thirteen X plus twenty. So 6X to the third minus thirteen X squared—I’m just checking all the choices—minus thirteen X plus twenty that’s choice B. Problem eleven —problem eleven, and if they wrote —they wrote minus 2, this is problem eleven just you know what we’re doing, minus 2X squared plus 6X plus 1 minus 2 times 4X squared minus 3X plus 1 is equal to— why not we just to simplify this—we rewrite this part, this is minus 2X squared plus 6X plus 1 and now we have to distribute this—I’ve you know let’s just distribute a minus 2 so minus 2 times 4X squared is minus 8X squared, that’s that, minus 2 times minus 3X, that’s plus 6X, minus 2 times 1 is minus 2 and now let’s see we can add the like terms up—let’s see what this is equal to—let’s do the X squared term so first I’ll do the minus 2X squared and minus 8X squared so that is minus 2 minus 8 that’s minus 10X squared. Let me do another color for each of them.
And then I have the X term that X —6X and then I have another 6X, you add them together you get 12X plus 12X and then you have your one’s term here X to the zeroth power you could view it. You have plus 1 and minus 2 so that’s minus 1 and then that is choice—let’s see, let me scroll down—that is choice D, minus 10X squared plus 12X minus 1, choice D. Problem number twelve—problem twelve rock and roll! Its problem twelve, which expression is equivalent to so now they’re multiplying they write 6Y squared minus 2 times 6Y plus 2. I always find it easier to—I mean you could do this in your head and you could—you should practice doing it in your head but if you never wanna make a mistake you just write it like this, 6Y squared, and I have nothing in the X’s spot and I say minus 2 and then this one is 6Y, I’ll write that in the Y’s spot—this Y squared, this is Y, this is Y to the zero which is 1 plus 2 and now I’ll multiply them. 2 times minus 2 is minus 4, 2 times 6Y squared is twelve Y squared right? So I’ll that in that spot, 12Y squared. Now 6Y times minus 2 is minus 12Y so that would go here, minus twelve Y and 6Y times 6Y squared is 36Y to the third—36Y to the third, so we have our answer, it is, you just add them up, thirty six Y to the third plus twelve Y squared minus twelve Y minus 4 and that is choice D.
And you could do this in your head and that’s a good thing to practice but I just wanted to make sure it was clean when I did. And let’s see, should continue with the next video or should I stop there because I’ve met eleven minutes. I’ll stop there and I’ll see you in the next video.
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