Suppose that 2^n − 1 is prime. Show that n must also be prime. (Hint: try to find a convenient factorization of the polynomial x^n − 1 if n is composite).

Q: x - 1 is a factor of x^100 – 1. O False O True O none of the choices

A: x100-1

Q: The expansion of (1 - x)® = A 1+4x - 7x² + . B 1- 4x + 7x2 - C 1+ 4x - 7x2 + Đ 1- 4x + 7x² – 23.

A: Please see the explanation below

Q: 3. What is the leading coefficient in this polynomial ? -7x^3 + 5x^2 + 8x^4 - 9x^7 - 15 -7 -9 -15

A: From the given equation , first we find the degree of the equation Degree is 7 So the coefficient…

Q: Create a cubic expression that when divided by (x-1) will have a remainder of 6

A:

Q: ind witnesses to show that n^3 − 5n^2 − 4n is O(n^3).

A: In this question, order of polynomial can be found with the help of Big-O notation. Big-O Notation…

Q: Evaluate (6 – 5)^2 by working within the parentheses first. Evaluate 6^2 – 5^2. Compare the answer…

A: Evaluate (6 – 5)^2 Evaluate 6^2 – 5^2.

Q: 80. A third-degree polynomial has two turning points. fx)=x3 false

A: We need to prove given statement is false.

Q: A polynomial has a leading term -2x^7. Discuss the end behavior

A:

Q: 4. (07.01, 07.02 HC) Part A: Create a third-degree polynomial in standard form. How do you know it…

A: (i) The standard form of the polynomial  p(x)=∑i=0naixi=anxn+an−1xn−1+an−2xn−1+.......+a1x+a0 Here,…

Q: Write out the first three terms in the expansion of (x + y)^20

A:

Q: Find the term that contains x^8 in the expansion of (3x-1)^11

A:

Q: (8p^3-38p^2-17p+43)÷(p-5) * 8p2+2p-7, R 8 8p2+p-9, R 9 O 8p2+p-5, R 13 O 8p2+p-10, R 4 O O O O

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Show the following for [im 11x|lp = 11x11.00 P-0 XER

A:

Q: Which of the following is the factored form of x^3 + 3x^2 – 10x – 24? * - O (x - 4)(x – 3)(x – 2) O…

A: Let f(x) = x3 + 3x2 - 10x - 24

Q: What is the coefficient of (x^8)(y^12) in the expansion of (2x+3y)^20

A:

Q: Expand (x − 1)^5 using any method of choice

A:

Q: The first three terms in the expansion of (1 + ay)^n are 1, 12y, and 68y^2. Find a and n.

A:

Q: Given that 3 is a zero of the polynomial P(x) = 2x+ – 17x3 +52x² – 64x + 21, find the other real and…

A: NOTE: Refresh your page if you can't see any equations. . take P(x)=0 the given zero is x=3,  now…

Q: What is the degree of the largest irreducible factor of (x^12)-1 over ℚ?   3 4 6 None of the above

A:

Q: Find the x^2y^3 term in the expansion of (3x + y)^5. Simplify your answer so it does not include any…

A: Given that (3x+y)5

Q: If the result of a polynomial division is  2x^3-4x^2-5x+23/X+2 make at least three definitive…

A: Given result of the polynomial is- 2x3-4x2-5x+23x+2 Here, Quotient = 2x3-4x2-5x Remainder = 23…

Q: A real number is called quadratic when it is a root of a degree two polynomial with integer…

A: Solution: At first we go through the below theorem. Theorem:    A countable union of countable sets…

Q: When you perform polynomial long division on the rational expression a²+3x+3 the numerator of the…

A: The rational expression,    x2+3x+3x+1

Q: Find the least positive integer that Yields the remainders 1,3 and 5 when divided by 5, 7, and 9…

A: