Theorems

Could someone explain the following to me. I got answers but just wanted to confirm. Help is surely appreciated, thanks!

1)Use the remainder theorem and the factor theorem to determine whether (y-3) is a factor of (y^4 + 2y^2 - 4)

A. The remainder is 0 and, therefore, (y-3) is a factor of (y^4 + 2y^2 - 4)
B. The remainder is 0 and, therefore, (y-3) isn't a factor of (y^4 + 2y^2 - 4)
C. The remainder isn't 0 and, therefore, (y-3) is a factor of (y^4 + 2y^2 - 4)
D. The remainder isn't 0 and, therefore, (y-3) isn't a factor of (y^4 + 2y^2 - 4)

2) Use the remainder theorem and the factor theorem to determine whether (b+4) is a factor of (b^3 +3b^2 - b+12)

A. The remainder is 0 and, therefore, (b+4) is a factor of (b^3 +3b^2 - b+12)
B. The remainder is 0 and, therefore, (b+4) isn't a factor of (b^3 +3b^2 - b+12)
C. The remainder isn't 0 and, therefore, (b+4) is a factor of (b^3 +3b^2 - b+12)
D. The remainder isn't 0 and, therefore, (b+4) isn't a factor of (b^3 +3b^2 - b+12)

3) Use the remainder theorem to determine the remainder the remainder when 3t^2 +5t -7 is divided by t-5 (I don't know what I'm doing but the answer is coming out wrong. I'm doing exactly what the example says)

4) Use the remainder theorem and the factor theorem to determine whether (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)

A. The remainder is 0 and, therefore, (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)
B. The remainder is 0 and, therefore, (c+5) isn't a factor of (c^4 +7c^3 +6c^2 -18c+10)
C. The remainder isn't 0 and, therefore, (c+5) is a factor of (c^4 +7c^3 +6c^2 -18c+10)
D. The remainder isn't 0 and, therefore, (c+5) isn't a factor of (c^4 +7c^3 +6c^2 -18c+10)

Using the "double-negative theorum of english" :D answers "A" and "D" (for all of them) are the same are you allowed to choose 2 answers?

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Originally Posted by Quick

Using the "double-negative theorum of english" :D answers "A" and "D" (for all of them) are the same are you allowed to choose 2 answers?

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You made a mistake. They are not the same. In fact all 4 statements are independant from each other. (If you taken from high school logic you can confirm this by creating a bi-conditional statement you will see that no tautoligies are formed).

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Originally Posted by ThePerfectHacker

You made a mistake. They are not the same. In fact all 4 statements are independant from each other. (If you taken from high school logic you can confirm this by creating a bi-conditional statement you will see that no tautoligies are formed).

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I misread the question as "if than" statements. If they had been than they would be the same...

A. IF The remainder is 0 and, than, (y-3) is a factor of (y^4 + 2y^2 - 4)
D. IF The remainder isn't 0 and, than, (y-3) isn't a factor of (y^4 + 2y^2 - 4)

answer "A" implies that when the remainder is zero, than (y-3) is a factor of (y^4 + 2y^2 - 4)

answer "D" implies that when the remainder isn't zero, than (y-3) isn't a factor of (y^4 + 2y^2 - 4)

you can see how they say the same thing if they were if than. but they're not :(

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I can only choose one answer.

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Originally Posted by The_Hot_Chick

I can only choose one answer.

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the answer is going to be either A or D, B and C are both nonsense, would you show me the "factor theorum" I have never heard of this, (it's probably just what your teacher calls it)