What should be added in the polynomial x3 6x2 11x 8 so that it is completely divisible by X² 3x 2? ✅ Đầy đủ
Kinh Nghiệm Hướng dẫn What should be added in the polynomial x3 6x2 11x 8 so that it is completely divisible by X² 3x 2? 2022
Họ và tên học viên đang tìm kiếm từ khóa What should be added in the polynomial x3 6x2 11x 8 so that it is completely divisible by X² 3x 2? được Update vào lúc : 2022-10-03 23:50:33 . Với phương châm chia sẻ Kinh Nghiệm về trong nội dung bài viết một cách Chi Tiết 2022. Nếu sau khi Read Post vẫn ko hiểu thì hoàn toàn có thể lại Comment ở cuối bài để Tác giả lý giải và hướng dẫn lại nha.Video transcript
Divide x squared minus 3x plus 2 divided by x minus 2. So we're going to divide this into that. And we can do this really the same way that you first learned long division. So we have x minus 2 being divided into x squared minus 3x plus 2. Another way we could have written the same exact expression is x squared minus 3x plus 2, all of that over x minus 2. That, that, and that are all equivalent expressions. Now, to do this type of long division-- we can call it algebraic long division-- you want to look the highest degree term on the x minus 2 and the highest degree term on the x squared minus 3x plus 2. And here's the x, and here's the x squared. x goes into x squared how many times? Or x squared divided by x is what? Well, that's just equal to x. So x goes into x squared x times. And I'm going to write it in this column right here above all of the x terms. And then we want to multiply x times x minus 2. That gives us-- x times x is x squared. x times negative 2 is negative 2x. And just like you first learned in long division, you want to subtract this from that. But that's completely the same as adding the opposite, or multiplying each of these terms by negative 1 and then adding. So let's multiply that times negative 1. And negative 2x times negative 1 is positive 2x. And now let's add. x squared minus x squared-- those cancel out. Negative 3x plus 2x-- that is negative x. And then we can bring down this 2 over here. So it's negative x plus 2 left over, when we only go x times. So then we say, can x minus 2 go into negative x plus 2? Well, x goes into negative x negative one times. You can look it right here. Negative x divided by x is negative 1. These guys cancel out. Those guys cancel out. So negative 1 times x minus 2-- you have negative 1 times x, which is negative x. Negative 1 times negative 2 is positive 2. And we want to subtract this from that, just like you do in long division. But that's the same thing as adding the opposite, or multiplying each of these terms by negative 1 and then adding. So negative x times negative 1 is positive x. Positive 2 times negative 1 is negative 2. These guys cancel out, add up to 0. These guys add up to 0. We have no remainder. So we got this as being equal to x minus 1. And we can verify it. If we multiply x minus 1 times x minus 2, we should get this. So let's actually do that. So let's multiply x minus 1 times x minus 2. So let's multiply negative 2 times negative 1. That gives us positive 2. Negative 2 times x-- that's negative 2x. Let's multiply x times negative 1. That is negative x. And then x times x is x squared. And then add all the like terms. x squared, negative 2x minus x-- that's negative 3x. And then 2 plus nothing is just 2. And so we got that polynomial again.
Nội dung chính- Video transcriptWhat should be added in the polynomial x3 6x2 11x 8 so that is completely divisible by x2 3x 2?What should be added to the polynomial x2 5x 4?Is completely divisible by XA when?
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what must be added to $x^3-6x^2+11x-8$ to make a polynomial having factor $x-3$?
If the required expression to be added be $K$ then $x^3-6x^2+11x-8+K$ is exactly divisible by $x-3$ but how do I find $K$??
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what must be added to $x^3-6x^2+11x-8$ to make a polynomial having factor $x-3$?
If the required expression to be added be $K$ then $x^3-6x^2+11x-8+K$ is exactly divisible by $x-3$ but how do I find $K$??
asked Jan 28, 2022 7:49
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We need to add some constant $k $ such that the polynomial $p (x)+k $ is divisible by $(x-3) $, that is, having $3$ as one of its factors. Thus, $$p (3)+k =0$$ $$Rightarrow (3)^3-6 (3)^2+11 (3) -8 +k =0$$ $$Rightarrow boxed k = 2 $$ Hope it helps.
answered Jan 28, 2022 7:54
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Let $f(x)=x^3-6x^2+11x-8+K$
By factor theorem, $f(3)=0$
$27-54+33-8+K=0$
$K=2$
answered Jan 28, 2022 7:55
L ParkerL Parker
3162 silver badges11 bronze badges
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Plug in $x=3$ into the polynomial you get $-2$, so you must add $2$ to it to make the polynomial zero $3$.
answered Jan 28, 2022 7:54
SarahSarah
1114 bronze badges
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Let $f(x)=x^3-6x^2+11x-8$.
Hence, $f(x)=q(x)(x-3)+f(3)$, where $q$ is a polynomial with degree two.
Thus, we need to add $-f(3)=2$.
answered Jan 28, 2022 7:59
Michael RozenbergMichael Rozenberg
186k30 gold badges151 silver badges265 bronze badges
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I think you know when to add term and when to subtract term from polynomial.
So continue from that.
Remember that if we have given some factor then you can find value of variable from that factor and can put in polynomial. This is equal to either 0 if any remainder not given else equal to remainder.
We (x-3) as a factor. So x-3=0.
x=3.
Put value of x as 3 in polynomial and you have value of k.
answered Jan 28, 2022 11:59
Kanwaljit SinghKanwaljit Singh
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What should be added in the polynomial x3 6x2 11x 8 so that is completely divisible by x2 3x 2?
Sice Remainder = 14 to make it 0- 14 should be added What should be added in the polynomial `x^(3)-6x^(2)+11x+8` so that it is completely divisible by `x^(2)-3x+2?`What should be added to the polynomial x2 5x 4?
The number to be added is 2.Is completely divisible by XA when?
D. Explanation: For every natural number n, (xn - an) is completely divisible by (x - a). 74. ... Exercise :: Numbers - General Questions.. Tải thêm tài liệu liên quan đến nội dung bài viết What should be added in the polynomial x3 6x2 11x 8 so that it is completely divisible by X² 3x 2?