Question
1.) Suppose the area of the rectangle is10x^3+37x^2+42x+30 and the length is 2x+5. What is the widthof the rectangle?2.) Use the factor theorem to find all the zerosf(x)=x^3-3x^2-16x+48 given that (x-4) is a factor.
1.) Suppose the area of the rectangle is 10x^3+37x^2+42x+30 and the length is 2x+5. What is the width of the rectangle? 2.) Use the factor theorem to find all the zeros f(x)=x^3-3x^2-16x+48 given that (x-4) is a factor.
Answers
1.) Suppose the area of the rectangle is 10x^3+37x^2+42x+30
and the length is 2x+5. What is the width of the rectangle? 2.) Use the factor theorem to find all the zeros f(x)=x^3-3x^2-16x+48
given that (x-4) is a factor.
Okay and discussion the area of the rectangle can be represented by. So area is given six X square plus 19 X plus 10. Okay If the length is given so L. Is given to X plus five. What is that? Okay we have to find out with so no problem. We know that area as it was to length, multiplied by weight from here. Where it will be area divided by length. So we have to divide this area by this length. Okay? It means we have to solve area by A by L. That is six X square plus 19 X plus 10 divided by two X plus five. Okay, this will be our fourth understand and now we have to divide this numerator, it is polynomial. Denominator is also polynomial. So to solve this we will use the method. Long division. Okay here, dividend 36 X squared plus 19 X plus 10 and divisor two X plus five. Okay and how we solve this customer dividend divided by first time off. Divisor six X squared divided by two X. That will be three X. Three X. Is the first time of the question. Three X. Multiplied by these two X plus five. It will be six X squared plus 15 X. Okay. And now subsection minus minus six X squared minus six X square zero 19 X minus 15 X. That is four X. And plus 10 from here. Okay. And now for is divided by it works. That is too. So it will be too and now two multiplied by two X plus five. It will be four X plus 10 Knaus obstruction. It will be zero and zero. So zero is the reminder. So the question will be the answer of this division or we can say w will be three X plus two. Okay, this is our question. So the worth of the rectangle can be represented by three x plus two. Thank you.
Okay, so we asked the factor. We see that these two times here haven't x squared in common. So we get exposed for and in these two turns out of five in common. So compact out of five. And I get expert sport. Now we have a express for in common that we can factor out. So we gotta experts for times x squared plus five.
Divide this by long division. And let me remind you we're going to really focus on this first term and how many times it takes to go in there? So what do we multiply two X squared by to get six X to the fourth? That would be three X squared. So I'm going to distribute that there and we're going to get six X to the fourth and then were distributed to that whole thing minus three X squared. And that three X squared is going to have to go over here. Now what we forget a lot of times is that minus students get that right? But that minus gets distributed here so we end up with two acts squared. Now we're going to have to bring down our four execute from there and that's positive. So now we're gonna do the same thing. What do I multiply this by to get four X cubed? Well we're gonna multiply by two X. And let's distribute this two X To everything there. So we have four x. cute -2X. And that means that goes over there and when I do that and now remember this is negated that's gone. We're going to bring down the two X. Square and the minus two X. M plus two X is gone. So now we're gonna bring down the -1. How many times is two x square to go into two X. One time. And when we subtract those We're gonna remainder of zero. So that is our answer.
So the perimeter of this rectangle is 26 X plus 16. You know, the perimeter is two times our base plus two times their height. And then for the area we know that it is 42 x squared plus 51 X plus 15 in our area is base times height. We want to find the dimensions are being R h. So for a permanent weaken divide off to here on both sides, everything is even so that would be 13 eggs plus eight equals B plus h and weaken saw for either beer H, it doesn't matter. So I'm just gonna suffer h So have 13 X plus eight minus B equals H. I'm gonna plug in that for my h and this other equation I have over here. So that would be 42 x squared plus 51 eggs plus 15 equals B times 13 X plus eight of minus B