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Would someone help me understand the method to this question
The cubic polynomial f(x) is defined by f(x)=x^3+x^2−11x+10
It can be shown that (x−2) is a factor of f(x).
Hence solve the equation f(x)=0, giving each root in an exact form.
(6 marks)
The cubic polynomial f(x) is defined by f(x)=x^3+x^2−11x+10
It can be shown that (x−2) is a factor of f(x).
Hence solve the equation f(x)=0, giving each root in an exact form.
(6 marks)
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#2
(Original post by The Big "R")
Would someone help me understand the method to this question
The cubic polynomial f(x) is defined by f(x)=x^3+x^2−11x+10
It can be shown that (x−2) is a factor of f(x).
Hence solve the equation f(x)=0, giving each root in an exact form.
(6 marks)
Would someone help me understand the method to this question
The cubic polynomial f(x) is defined by f(x)=x^3+x^2−11x+10
It can be shown that (x−2) is a factor of f(x).
Hence solve the equation f(x)=0, giving each root in an exact form.
(6 marks)
is a factor... so, by the Factor Theorem, one of the roots is...??Now use polynomial division to divide
by 
to obtain a quadratic. Solving this quadratic will yield the other two roots.
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#3
If you want to show it's a factor, sub x=2 in and show f(2)=0.
Otherwise, divide the cubic by x-2. Then the other two factors are given by factorising/solving the quadratic quotient.
Otherwise, divide the cubic by x-2. Then the other two factors are given by factorising/solving the quadratic quotient.
(Original post by The Big )
Would someone help me understand the method to this question
The cubic polynomial f(x) is defined by f(x)=x^3+x^2−11x+10
It can be shown that (x−2) is a factor of f(x).
Hence solve the equation f(x)=0, giving each root in an exact form.
(6 marks)
Would someone help me understand the method to this question
The cubic polynomial f(x) is defined by f(x)=x^3+x^2−11x+10
It can be shown that (x−2) is a factor of f(x).
Hence solve the equation f(x)=0, giving each root in an exact form.
(6 marks)
1
reply
(Original post by RDKGames)
is a factor... so, by the Factor Theorem, one of the roots is...??
Now use polynomial division to divide by to obtain a quadratic. Solving this quadratic will yield the other two roots.
is a factor... so, by the Factor Theorem, one of the roots is...??Now use polynomial division to divide
by to obtain a quadratic. Solving this quadratic will yield the other two roots.
0
reply
(Original post by RDKGames)
is a factor... so, by the Factor Theorem, one of the roots is...??
Now use polynomial division to divide by to obtain a quadratic. Solving this quadratic will yield the other two roots.
is a factor... so, by the Factor Theorem, one of the roots is...??Now use polynomial division to divide
by to obtain a quadratic. Solving this quadratic will yield the other two roots.
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reply
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#6
(Original post by The Big "R")
The quadratic i got was x^2 + 3x -5 when dividing and i get -3 + and - root29 divided by 2. However i dont understand what you mean by the first point x-2 is a factor?
The quadratic i got was x^2 + 3x -5 when dividing and i get -3 + and - root29 divided by 2. However i dont understand what you mean by the first point x-2 is a factor?
being a factor of a polynomial 
means this polynomial can be rewritten as 
where 
is a different polynomial.The solutions to
are given by 
or 
. Clearly, 
is a solution to the first factor. To solve you first need to know what even is, which is obtained by
.This is why you need to divide R(x) by x-2.
The Factor Theorem, which you should probably be aware of if you're doing a question like this, says that if
is a factor of a polynomial , then we must have 
, meaning 
is a root.
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