11. Determine a general rule to help decide whether xa and x + a are factors of I x - a" and x" + a".

Q: . What is the coefficient of a" in (2 – x)"?

A:

Q: 6. a. Find the two integers whose difference is 2 and whose product is 18. Let x-a number Let…

A:

Q: Let p > 2 be a prime number. If f(x) = 1' + x* + x² - x +1 € Z,[F] is divisible by the polynomial z…

A:

Q: In Exercises 13–16, find y′ (a) by applying the Product Rule and (b) bymultiplying the factors to…

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: Apply u-substitution

A: We have to find the integration using u-substitution: ∫4ln1xxdx Rewriting the integration using…

Q: For А - 2аx + Зау + az and В %3 5аx - 2ау - az OAB is:

A:

Q: Show that if x > 0 and |x² – 9| < 2, then |x - 3| < 1.

A:

Q: 8. Use finite differences method to classify the following relations as linear, quadratic or…

A: In this question, the concept of the finite differences method is applied. Finite Difference Method…

Q: 1. Differentiate. Show your work to get credit. a) g(x) = x* In(2.x² +7) by using the product rule.

A: SInce multiple subparts are asked, I am ansering only first 3

Q: var(û), if û = X1 + a jg X (n-1) + (X2 ++X(n-2) + 3 6X(m-1) + 증 .. 2(n-3) 4. 29n 256(п-3) 29…

A:

Q: Show that x19 + x8+ 1 has multiple zeros in some extension of Z3.

A:

Q: 15. Find x so that m || n. (5x – 20)°

A:

Q: Find the Dervative of 23 x2 - 2x find r %3D

A: Given  Now first derivative is

Q: Q\ Determine a condition on |x - 1| that will assure that * 1 |x² – 1| <

A:

Q: Q\ Determine a condition on |x - 1| that will assure that * 1 |x² – 1| < |3

A: Given that |x2-1|&lt;13 That is -13&lt;(x2-1)&lt;13

Q: In(x-1) 33 Differentiate with respect to x. 2x + 3

A:

Q: Find the coefficient of x5 y8 in (x + y)13.

A: Binomial theorem(x+y)n=∑j=0nnjxn-jyj

Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: Show that whether x5 + 10x3 + x + 1 is O(x4) or not?

A:

Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: Verify that 5 18 11 2²4 ахду 22+ дуох - for f(x, y) = 2x³y6 - 4x5y4.

A:

Q: Find positive integers that satisfy x + y + z = 6 x + 5y + 8z = 35 x = i ! y = i

A:

Q: Does S = {x² + 1,x² – 1, 2x – 1} span P2?

A: we know dimension of P2 is 3 so any set which span P2 must have at least 3 elements. here given set…

Q: Prove that the expression 2y2 - 128 is equal to 2(x2+2) (x² – 2) (x³ + 4x* + 16).

A:

Q: 43. Show that there cannot exist rational numbers a, b such that V3 = a+b/2.

A:

Q: Express as a polynomial. (2u +3)(u - 4) ( 4u+u ) 2

A: Given: y=22u+3u-44u+u For expressing given expression as a polynomial, we simplify given expression…

Q: 5. Show that Ax) = Inx² - 1- In/3, if f'(x)= and (2) = 0. x- 1 Justify your answer.

A: To show that f(x)=ln|x²-1|-ln√3

Q: c. Find all the points X1 x2 in R3 [x3. that are transformed to Explain.

A: Given, the transform spantial coordinates                               x1x2x3into plane coordinate…

Q: Prove that if 8x-5=-2x-15 then -x=1

A:

Q: 2) Show that a3 + b³ = (a + b)(a² – ab + b²) is a polynomial identity. %3D |

A: Start with Right hand side as follows.

Q: Find the term of (x + +)° that does not contain x.

A: Given expression is, x+1x6. The general term is given by, Cknakbn-k. In the given expression,…

Q: What is the coefficient of x 9 in (x 3 + x) 5?

A: What is the coefficient of x9 in x3+x5.

Q: Show that 1 -2 = R³. span 3 1

A: In R^3 if three vectors are linearly independent then they span the whole space R^3.

Q: Express as a polynomial. (3u - 1)(u + 2) + 7u(u + 1)

A: Given expression: 3u-1u+2+7uu+1

Q: of “a” if (x2/3)(x1/4) = xa

A: The function is given as x23x14=xa. Simplify the expression to find the value of a. x23x14=xa Apply…

Q: Suppose that x = (150y +45) where x and y are integers. What are the common dividers of x and 150.…

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Q: 13. Select all the products that are less than x 5. X5 9x는 @ e x 4

A:

Q: 4. Which of the following describes the end behavior of the polynomial y = -x+ x? A as x -oo, y 00…

A:

Q: Prove that F (3x)(A → B) → ()A → (3x)B.

A: We have to prove, ∃xA→B→∀xA→∃xB

Q: verify that 5A = 3A + 2A

A: Given that A=341127. Compute 3A+2A as follows.

Q: Prove that ax² bx + (x − a) (x −b) (x −c) ¹ (x − b) (x − c) || x³ 3 (x-a)(x-b)(x-c) C +—+1 X-C

A:

Q: Prove that x3 x7

A: we have to prove

Q: Suppose that ƒ'(x) = 2x for all x. Find ƒ(2) if ƒ(1) = 0

A: We have, f'x=2x Integrating both of the side with respect to x, we get the result as…

Q: Prove that the expression 2y2 - 128 is equal to 2(x2 + 2) (x² – 2) (x³ + 4x* + 16)

A: a3-b3=(a-b)(a2+ab+b2)a2-b2=(a+b)(a-b)

Q: 15. Show that (x+ 5) is a factor of f(x) =x3 -x² -21x + 45 then factor f (x) completely.

A:

Q: Use intermediate theorem to explain P [x] = x* – x' – 10 has a zero in [2, 3]

A: According to intermediate value theorem of a function f(x) is continuous on [a, b] and L is any…

Q: Suppose that ƒ′(x) = 2x for all x. Find ƒ(2) if a. ƒ(0) = 0 b. ƒ(1) = 0 c. ƒ(-2) = 3.

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Q: If 2sin-1x = n, what is x?

A:

Q: 29. For |x|<1, prove that 16x 24x 8x 1 + 1-x1+x 1-x ..... .. 8x 8x = 1+ (1- x)? (1+x)²' (1-x)?

A: