Example 1:
2. let's divide [(x square) plus (5x) plus 6] by (x plus 2). So, we're going to put the (x plus 2) on the outside and the (x sqaure) plus (5x) plus 6 on the inside.
3. The denominator should go on the outside, The frirst thing we know to do is divide (x square) divided by x is equal to x. x sqaure divided by x is basically x, we need to do is subtract the exponents two minus one is equal to one.
4. now after you divide the next step is to multiply, let's put a negative sign and parenthesis. Everything that's going to bo written here we need to distribute by a negative sign or basically just change the sign.
5. if we multiply x by x that is equal to x square and if we multiply x by positive 2 that's equal to positive 2x.
6. At this point subtract, x square minus x square those will cancel and it's equal to zero. Next 5x minus 2x is equal to positive three x, six minus nothing is basically equal to six.
7. So you could bring down the six, Now, the next thing that we need to do is divide. We're going to follow the same street step as we did before.
8. We're going to divide multiply and subtract. 3x divided by x that's equal to positive 3. and then now we're going to multiply, 3 times x is 3x and then 3 times 2 and that's equal to positive six so now we can subtract.
9, Three x minus three 3 is zero, six minus six is zero, so the remainder is zero.There the solution is what we see here.
10. x square plus five x plus six divided by x plus 2 that's equal to x plus three. That's the answer.
https://www.youtube.com/watch?v=_FSXJmESFmQ
Example 2.
1. Let's work another example, try this one. Divide (2x cube) plus (8x squared) minus (6x) plus 10
go head and divided by x minus two.
2. So feel free to pause the video and work on this example, So first let's write it out.
3. Now the first thing we're going to do is we're going to divide.
4. Let's divide 2x cubed by x so that's equal to 2x squared, next let's multiply. 2x squared times x that's equal to 2x cubed, the first one is always going to be the same, these two should always match and then 2x squared times negative 2 that's equal to negative 4x squared.
5. So now, let's subtract, 2x cubed minus 2x cubed and those two will always cancel and so that's zero.
6. 8x squared minus negative 4x is basically the same as 8x squared plus 4x squared and that's equal to positive 12x squared.
7. Now everything else, we're just going to bring it down to the next level. So we have negative 6x and positive 10.
8. Now let's repeat this three steps: Divide and multiply and subtract.
9. So let's divide 12x squared by x. so that 's equal to 12x.
10. Now let's multiply. 12x times x that's a 12x squared and 12x times negative 2. that's equal to negative 24x . Now let's subtract.
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11. We have 12x squared minus 12x squared which is equal to zero and negative 6x minus 24x which is the same as negative 6x plus 24x. that's positive 18x.
12. Now let's bring down the 10,so we have 18x plus 10. So now let's divide 18x devided by x is positive 18 and then multiply 18 times x is 18x and 18 times negative 2 that's negative thirty six. So now let's subtract 18 minus 18 is zero.
13. And ten minus negative thirty-six. We have two negative sign. That's the same as ten plus 36. Ten plus 36 is fourty six.
14. Now we can't divide 46 by x. So the remainder is 46. So how do we write the answer. Whenever we have remainder. So it's going to be what you see here plus the remainder which is 46 divide by what you try to divide it by which is x minus 2.
15. So therefore the final answer is 2x squared plus 12x plus 18 plus 46 divided x minus 2. So all of that is equal to 2x cubed plus 8x squared minus 6x plus 10 divided by x minus 2. So this is the answer.
16. Now let's move on to our next problem, Go head and divide 6x to the fourth minus 9x squared plus 18 divided by x minus three.
17. So take a minutes pause the video and work on the problem and once you have a solution unpause it to see if you have the right answer.
18. and Be careful with this one. So let's put the x minus 3 on the outside and let's put the numerator on the inside. Now we need to put it in standard order. it's 6x to the fourth now we can't forget about the zero x cubed. so plus zero x cubed and then minus 9x squared and don't forget about the zero x, and finally plus eighteen.
19. So we're gonna follow the same three steps. Divide, Multiply and subtract.
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https://www.youtube.com/watch?v=_FSXJmESFmQ
