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Guys welcome to my channel matami find the reminder when the given polynomial is divided divided by x minus 1. Guys. Here.
I am going to show you two approaches is long division method and the second one is applying the remainder theorem. Okay. So the first attempt is the long division method.
So here. I am going to divide the given polynomial with x minus. 1.
Okay. So im writing the polynomial x. To the power of 4 plus x.
Cubed. Minus 2x square. You know.
Few of the questions are the examiner will be very particular to apply the long division method. Then you can approach this method. Okay.
Now here i am doing a rougher guys just focus on x to the power of 4. So write that and the first element of the x minus. 1.
Which is x now divide this one and the remainder is x cube. Now take this x cube and put it in the quotient. Now.
Multiply x. Cube. With x minus.
1. Youll be getting x to the power of 4 minus x. Cube.
The signs minus x. To the power of 4 plus. X cube.
These two get cancelled and now add them to x cube. Now get a style rest of the elements. Which is minus 2x square plus x plus 1.
Now focus on 2x cube. And im doing a refer guys divided by x okay. Now and what is the remainder 2x square.
Now take this 2x square and write in the quotient plus 2x square now multiply 2x square with x minus 1. So 2x cubed minus 2x square now change the signs these two get cancelled and here again so youre left with. X plus.
1. Now x. X.
One. Time. So right.
Plus 1 x. Divides. With x.
How many times. One. Time.
So. Right. Plus.
1. There. Now.
X. Minus. 1.
With. 1. And.
The answer. Is x. Minus.
1. Now. Change.
The signs and plus x. Minus. X.
Get cancelled and 1 plus. 1. Is 2.
And that is the remainder and we have done this entire process using the long division method now let us apply the reminder theorem whether we are going to get the same values or not okay. Here. The dividend.
Divisor is x. Minus. 1.
Right. Now x minus. 1.
When equated to 0 x. Value. Would be plus.
Why because minus 1 goes to the right hand side. Now. Take this x value and replace.
In the p of x and p of x. Is nothing. But a imaginary representation of the polynomial okay so you can take anything because its a polynomial normally.
We will be taking p of x. And write the given polynomial. First and instead of p of x.
Now put. 1. Now 1 to the power of 4 is 1 and 1 cube.
Is 1 minus. 1 square. Is 1 multiplied with 2.
Is minus 2. Here. Now lets just check.
Here minus. 2. And plus 1 minus.
1. Get cancelled. What youre left with 1 plus.
1. Which is 2. Now this is your answer guys using the remainder theorem.
So its up to you which theorem to use and if the examiner is very particular to do in the long division method you can approach the left hand side otherwise for one more question you can even apply the remainder theorem. Still you will be getting full marks for that thats it guys if you like my explanation. Please dont forget to share and subscribe.
See you in the next video bye for now. .
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