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1. The polynomial f(x) is deﬁned by f(x) = x^3 − 9x^2 + 7x + 33.
Solve the equation f(x) = 0, giving each root in an exact form as simply as possible.
where do i even begin with this?
2. sub in values until you get a linear solution, then divide the cubic by the linear factor to get a quadratic, which you should then solve.
3. (Original post by an_atheist)
sub in values until you get a linear solution, then divide the cubic by the linear factor to get a quadratic, which you should then solve.
i got -53 as a remainder and x^2-11x+29 when i divided the f(x) equation by a factor of (x+2). does this seems right to you?
4. (Original post by Chelsea12345)
i got -53 as a remainder and x^2-11x+29 when i divided the f(x) equation by a factor of (x+2). does this seems right to you?
No. Try a different factor.
Subbing different values of x into f(x) might make the search easier (less working needed), then do the division when you find one that gives f(x)=0 (think about the factors of 33, that should give you a hint about where to look)
5. (Original post by Chelsea12345)
...
If you have a Casio fx83 calculator, I recommend you use the table of values feature for this.

Press Mode then 3: Table.

Type in (Use the red Alpha key and the right bracket key to get the x).

Start at -10. End at 10. Go up in steps of 1.

Look for when f(x) = 0. Say this is when x = k. This means is a linear factor so you will be able to divide by this linear factor to produce a quadratic quotient. Solve the quadratic using whatever method you choose.

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