what is the quotient (x3 + 6×2 + 11x + 6) ÷ (x2 + 4x + 3)? This is a topic that many people are looking for. amritsang.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, amritsang.org would like to introduce to you x3+6×2+11x+6 Factorise the given Polynomial. Following along are instructions in the video below:
Guys welcome to my channel masami factorize. The given polynomial x. Cubed.
Plus 6x square square plus. 11x plus 6. Guys.
It is a cubicle equation. Which has been given you the first step would be a trial and error method. So here.
Ill be taking the value of x. As plus or minus 1 plus. Or minus 2.
And so on till. I get zero of that give an equation ok so once i get the zero of the given equation. Then ill proceed further so here.
Ill be because in the given equation. There are all the positive symbols. So i will be taking x is equal to minus 1.
And i try to put in the given polynomial. If i could able to get. 0.
Then i proceed so here minus 1 q. Plus 6 multiplied with minus 1 square. Because im just replacing the value of x.
In the given equation ok.
And now minus 1 cube. Is minus 1. And minus 1 square is 1 so 1 into.
6. Is plus 6. And 11 multiplied with minus 1.
Is minus 11. And plus 6 add all the positives and the negative a lose the result is 0. So guys feel lucky that in our very first return that we got 0.
When x value is minus 1. Now push minus 1. To the left hand side.
You will be getting your first factor. Which is x plus. Ma.
Now take this x plus. 1. And divide.
The given polynomial. Ok. Now i am going to divide the given polynomial with the factor that we just got.
Which is x plus. 1. So i am writing the given polynomial here x.
Cubed plus 6 x.
Square plus 11 x. Plus 6. And now so it is x square times x square.
Multiplied with x is x. Cubed plus 1 into x square is x square. Now chain.
The symbols next cube get cancelled and here 6 minus 1 is 5 x square now bring down 11 xn 6. Now focus on phi x square so plus 5x times it gets divided now phi x multiplied with x is phi x. Square.
Phi x. Plus. I have sorry into 1 is phi x now change the symbols again phi x square.
Get cancelled and 11 minus. 5. Is 6x now bring down classics.
Now focus on this 6x. Say divides. 6.
Times 6 x. 6. Change.
The symbols and the resultant is 0. Now so because we got 0. It has exactly divided now focus on the quotient.
Which is a quadratic equation.
Guys. X. Squared.
Plus. 5x. Plus.
6. Is a quadratic equation. Now our immediate focus should be on splitting the quotient.
Which is x square. Plus. 5x plus 6.
Equal to 0. Split the middle term in such a way that the addition should be phi x. And the product should be 6x square three twos are right so 3x plus 2x plus 6.
Equal to 0. Now take x common well be getting x plus. 3.
And take plus two common well be getting x plus. 3. And now take x plus.
3. Common you will be getting the other factor. As well.
Which is expressly now therefore the fatness of the given.
Polynomial are the first one is x. Plus. 1.
Right. And the other two factors are x. Plus.
2. And x. Plus.
3. So right. First x.
Plus. 1. And right.
In a sequential order. X. Plus.
2. And x plus. 10.
And guys. This is your final answer. I hope you love loud my explanation.
If the answer is yes. Please dont forget to share and subscribe to my channel. Thank you very much bye for now you .
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