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lLovePhysics
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Here are some SAT II Math IIC Questions that I have. Fun!
I'm in the chapter of "Higher-Degree Polynomials" right now and I have some questions concerning some facts:
How do these work?:
1) "The Remainder Theorem- If a polynomial P(x) is divided by x-r (where r is any constant), then the remainder is P(r).
So does this mean if you choose any number, for example, 5 and then divide a polynomial (lets say [tex]x^{4}+x^{3}+3[/tex]) by x-5, the remainder will always be P(5)??
Is it beneficial to test these kind of things? In order to get these kind of problems, right you really need mathematical acumen right? Should I test these out to "prove" them to myself? I've tried with this one but I ended up messing up on long division =/
Also, if a polynomial has rationa coefficients, then will it always have irrational zeros? and if a polynomial has real coefficients, does it always have complex zeros? I know that both irrational zeros and complex zeros have conjugate pairs.
Are Irrational numbers most often seen as radicals or rationals or both? Thanks for your help in advance!
I'm in the chapter of "Higher-Degree Polynomials" right now and I have some questions concerning some facts:
How do these work?:
1) "The Remainder Theorem- If a polynomial P(x) is divided by x-r (where r is any constant), then the remainder is P(r).
So does this mean if you choose any number, for example, 5 and then divide a polynomial (lets say [tex]x^{4}+x^{3}+3[/tex]) by x-5, the remainder will always be P(5)??
Is it beneficial to test these kind of things? In order to get these kind of problems, right you really need mathematical acumen right? Should I test these out to "prove" them to myself? I've tried with this one but I ended up messing up on long division =/
Also, if a polynomial has rationa coefficients, then will it always have irrational zeros? and if a polynomial has real coefficients, does it always have complex zeros? I know that both irrational zeros and complex zeros have conjugate pairs.
Are Irrational numbers most often seen as radicals or rationals or both? Thanks for your help in advance!