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Factorising Polynomials

How would I go about solving this question (From May 09 MEI C1 Paper)

Show that 3 is a root of x3−5x2+2x+8=−4x^3 -5x^2 +2x +8 = -4
Hence solve this equation completely, giving the other roots in surd form
Original post by Chris654
How would I go about solving this question (From May 09 MEI C1 Paper)

Show that 3 is a root of x3−5x2+2x+8=−4x^3 -5x^2 +2x +8 = -4
Hence solve this equation completely, giving the other roots in surd form

Can you show that 3 is a root? (I'd first rearrange the equation into the form p(x) = 0, getting rid of the -4 from one side.)
Original post by Chris654
How would I go about solving this question (From May 09 MEI C1 Paper)

Show that 3 is a root of x3−5x2+2x+8=−4x^3 -5x^2 +2x +8 = -4
Hence solve this equation completely, giving the other roots in surd form


Do you know how to carry out traditional algebraic division or can you equate coefficients to divide polynomials?
Reply 3
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Chris654
OP
5
Yeah I showed that 3 is a root of say f(x) = -4 , however if I move the -4 to the left side and making it equal to zero becoming p(x) then surely 3 is no longer a root of it anymore?
Reply 4
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Chris654
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Original post by Mr M
Do you know how to carry out traditional algebraic division or can you equate coefficients to divide polynomials?


Yes I can do algebraic division, however I do it the grid method way, not by long division :/
Reply 5
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VannR
21
Use the factor theorem.

Show that f(3) = 0. By the factor theorem, this means that (x - 3) is a factor of the polynomial. By extension, this means that 3 must be a root of the equation.

Although this method is valid, you be being asked to use another method such as algebraic long division to show that the remainder when f(x) is divided by (x - 3) is 0. If you are allowed to use the remainder theorem, do so! It makes this kind of problem very straightforward.
Original post by Chris654
Yes I can do algebraic division, however I do it the grid method way, not by long division :/


Divide the cubic (rearranged so it is equal to zero) by (x-3) then.
Reply 7
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Chris654
OP
5
Thanks for the help everyone , got x= 1+- root 5 which should be correct
Original post by Chris654
Yeah I showed that 3 is a root of say f(x) = -4 , however if I move the -4 to the left side and making it equal to zero becoming p(x) then surely 3 is no longer a root of it anymore?


Of course it is still a root. rearranging an equation does not alter the roots.

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