If a polynomial with integral coefficients is reducible in the field of rational numbers, then the polynomial must have a rational root?

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• 1. Write me some laws of polynomials
• 2. How many terms are there at most and at least for a polynomial of degree 5 with only the letter Y? Why? Please help me answer My understanding is innumerable, the 5th power + 1 + 1 + 1 of Y. isn't + 1 also the 5th power polynomial of Y? Isn't my understanding right
• 3. Give me an example of a polynomial
• 4. If the m-th power of polynomial X and the 2-th power + (M + n) x + 1 of polynomial X are cubic quaternions and the coefficient of the first term is - 1, then M =?, n =?
• 5. The coefficient containing x ^ 3 in polynomial (1-2x) ^ 5 (2 + x) is? The answer is - 120, but I seem to have - 40,
• 6. If a = negative, B is not equal to 0, and N is a positive integer, then the following conclusion is correct: the 2nth power of a and the 2nth power of B are opposite to each other B: The N + 1 power of a is opposite to the N + 1 power of B. C: the n power of a is opposite to the n power of B. D: the 2n + 1 power of a is opposite to the 2n + 1 power of B Which one? Why?
• 7. Mathematics complete square formula 1. Known (x + y ^ 2) = 16, (X-Y) ^ 2 = 4, find x ^ 2 + XY + y ^ 2 2.（x-2y+3z）^2 3.[(2a+b)(2a-b)]^2 4. The side length of a square is a cm. Reduce the side length of the square by 6cm and increase it by 6cm respectively. What is the sum of the areas of the three squares?
• 8. If f (x) = one in X, X
• 9. If G (x) = e ^ x, X ≤ 0 = LNX, x > 0, then G (g (1 / 2))=
• 10. It is known that f (x) = ax LNX, X belongs to (0, e], G (x) = LNX / x, where e is a natural number and a belongs to R (1) The monotonicity and extremum of a = 1, f (x) are discussed (2) Verification: under the condition of (1), f (x) > G (x) + 1 / 2 (3) If there is a real number a, the minimum value of F (x) is 3. If there is, the value of a can be obtained. If not, the reason is given
• 11. It is proved that the polynomial f (x) = x ^ 3 + 3x + 1 is irreducible in the field of rational numbers College Advanced Algebra for help!
• 12. How to prove that all polynomials with rational coefficients are countable sets?
• 13. In the polynomial of X obtained by (3x + 32) & nbsp; 100 expansion, the terms with rational coefficients are______ Item
• 14. -The reciprocal of the opposite number of 1 and 1 / 3 is? The absolute value is 2 and 1 / 3? The ratio size ↓ 1 (- 4) 3-3-4 power
• 15. Exponents are the same, multiplication or addition? Add or multiply
• 16. Under what conditions should we try to add exponentially with the same base
• 17. Multiply by the power of the base, what if there is a number before the base For example: 2 (x + y) ^ 3 × (x + y) =? I know how to calculate the front one without 2, but I don't know if I add 2 Ask the prawns to help Please give the specific value
• 18. Proof: (1 + A + A ^ 2 +...) +a^n）^2-a^n=(1+a+a^2+… +a^n-1)(1+a+a^2+… +A ^ n + 1), where is n natural number
• 19. Let set a and set B be set n of natural numbers, and map f: a → B maps element n in set a to element 2n + N in set B, then under map f, the original image of image 20 is______ ．
• 20. Let a and B be set n of natural numbers, Mapping f: A to B maps element n in set a to element 2 ^ n + N in set B, then under mapping f, the original image of image 11 is