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# FP1- Writing polynomials as product of linear fraction watch

1. 'Write the following polynomial as products of linear factors'

9z^2 -6z +5

I'm not sure how to go about doing this question. The book only has examples where one of the factors have been given and then to work out the other factor. I could use the factor theorem but I doubt that will work because it has complex roots. My only other option is to use quadratic formula and I got 6 +or - root -144 all divided by 18. Which I think I can write as 1/3 + or - root -8. But I'm not sure how to turn this into a factor or if this is the right method. Any advice would be appreciated.
2. You have made a mistake with the formula. Try it again or complete the square.

If a quadratic has an answer x = k then a factor is (x - k). Does that help?
3. (Original post by Mr M)
You have made a mistake with the formula. Try it again or complete the square.

If a quadratic has an answer x = k then a factor is (x - k). Does that help?
Thank you, completing the square worked fine. Is it okay to turn these kind of questions into equations in the exams, you won't get docked marks or anything?

Also I have a similar question involving a cubic

z^3 +z -10

What method could I use for this?
4. (Original post by Freerider101)
Thank you, completing the square worked fine. Is it okay to turn these kind of questions into equations in the exams, you won't get docked marks or anything?

Also I have a similar question involving a cubic

z^3 +z -10

What method could I use for this?
Turning this into an equation as a step in your working is fine.

Regarding the cubic, can you guess a real factor to start you off? It is invariably -2, -1, 1 or 2.

Then write the cubic as (z - k)(Az^3 + Bz + C). Expand the brackets and you can find A B and C (you will be able to see what A and C are immediately). Then work on the quadratic as before.

Alternatively, as this is a depressed cubic, you could use various longwinded methods that look cool but are horribly inefficient.
5. (Original post by Mr M)
Turning this into an equation as a step in your working is fine.

Regarding the cubic, can you guess a real factor to start you off? It is invariably -2, -1, 1 or 2.

Then write the cubic as (z - k)(Az^3 + Bz + C). Expand the brackets and you can find A B and C (you will be able to see what A and C are immediately). Then work on the quadratic as before.

Alternatively, as this is a depressed cubic, you could use various longwinded methods that look cool but are horribly inefficient.
Thank you, I understand now- I just forgot that a cubic always had a real root!

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