(a) Find, in its simplest form, the product of a + bỉ and a- a®b³ + b%. (b) Given that 22r+2 × 5x-1 - 8*x 52r, evaluate 10*. %3D

Q: 3x° + x-10 37x+38 a) Show that 3x-12 + x2 + 4x+4 (x+2)

A: To show that, 3x3+x-10x2+4x+4=3x-12+37x+38x+22

Q: Which of the following is the correct complete factorization of x4 - 1?…

A: To find the complete factorization of x4-1. Solution: We know that, a2-b2=a+ba-b Factorizing the…

Q: In Z,[x] The quotient when 5x* + 3x² + 1 is divided by 3x² + 2x + 1 is 4x² + 3x + 6. a) True b)…

A: We decide whether given statement is true or false

Q: What is the result when 4x - 11a - 24x2 + 19x – 12 is divided by T(x) 4? If there is a remainder,…

A:

Q: 1 The rational expression can still be decomposed. (9x2 + 16)? A FALSE B) TRUE

A: The rarational expression in implicit form therefore cannot be decomposed

Q: If Z1=4+10i and Z2-11+19i, find the real part of the product Z1Z2 Give your answer as an integer.

A: See the details solution in below

Q: Is the polynomial x +x - 12x +3 divisible by x- 3?

A:

Q: Find the product. Express your answer in standard form. (-4 – 7)(V3 – 2i)

A:

Q: What is the coefficient x¹² in (x+2)¹⁵?

A: Find the coefficient of x12 in the expansion of x+1215. Using binomial theorem, find the expansion…

Q: 5. Multiply the polynomials (x + 3)(2x – 4). What is the product in the form ax? + bæ + c? Enter…

A:

Q: Which of the following polynomials is exactly divisible by (3x+1)? A. 6x2+17x+5 B. 9x2+6x+1 C.…

A: We have to check which of the given polynomials is exactly divisible by 3x+1. Factor theorem states…

Q: What is the coefficient of x16 in (2+x³ – xª)7 ? -

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Q: When fully multiplied out, what is the 8th term of (x – 3y)'³?

A:

Q: tions: Find the soluti 10x2 = 6x %3D

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Q: Determine the coefficients of the product: (2- 3)(2 – 2)(x – 1)= 23+

A: Solution:-  the given expression is  f(x)=(x-3)(x-2)(x-1)

Q: V. (a) Find the product of: 1. (x+2)(x + 2) 2. (2x – 1)(2x - 1) (b) Make a general rule about…

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Simplify the ratio of factorials. (8n - 1)! (8n + 1)!

A: Given            8n-1!8n+1!

Q: 1. The number of courses that Felix takes in this cycle is numerically equal to the number of prime…

A:

Q: 1 The rational expression can still be decomposed. (9x² + 16)? (A) TRUE B) FALSE

A: The term in the denominator (9x2+16)2 can not be factorized further because it will be of the form…

Q: Find the product: (2x + 5) (x2 - x + 2)

A: Given:To find the product: (2x + 5) (x2 - x + 2)

Q: Find the value of p for which x²– 4x2+ px-8 is exactly divisible by x- 4.

A:

Q: . What is the coefficient of ?^4 when (3+4x^2)^3 is expanded?

A:

Q: Find the coefficient of x11 in (x2 - 3x) / (1 - x )4

A: Solution:

Q: 17. Find the discriminant of 8x -x +7= 0.

A: topic - discriminanat

Q: Do the polynomials x³ + 2x – 4, x³ + x² – 3x + 1, and æ³ + 5 generate P3(R)? Explain. - -

A: Here generate means span.  The span of a set of vectors is the set of all linear combinations of the…

Q: Which of the following is the correct complete factorization of x4 - 1?…

A: Here we have to factorized,  =x4-1

Q: Which of the following is the correct complete factorization of x4 - 1? (x-1)^{2}(x+1)^{2}

A: Given, x4-1

Q: If k is a constant, what is the value of k such that the polynomial k?x3 - 6kx + 9 is divisible by x…

A:

Q: Find the product. (x-6)(x+6) O x²+12x-36 O x²+36 O x2-36 O ²-12x-36

A: On multiplying ,we get

Q: Prove the polynomial identity for the cube of a binomial representing a difference: (x-y)3=x³-3x?y +…

A:

Q: Eliminate the arbitrary constants for the ff: 3x2y - mx=3 Use elimination by forming PDE

A: Given the equation:3x2y-mx=3forming PDE by eliminating the arbitrary constantHere m is arbitrary…

Q: AB is a midesegment. find x. 3x + 30 2x + 8 В A 23 X =

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Q: Use any method to simplify the.complex fraction. k+4 12k 5k - 2 6k

A:

Q: 32. If k is a constant, what is the value of k such that the polynomial k2x3 - 6kx +9 is divisible…

A: If the polynomial is divisible by -1 then the remainder will be 0.

Q: Use synthetic division to solve 102 X+3 O 2x²-2x-29+- O 2x²-2x-29+102 O 2x³+10x²-5x O 2x²+10x-5…

A: We can find the answer in the below steps to find the correct answer.

Q: What is the coefficient of x12 in (x+2)14?

A: Given expression is,

Q: Multiply (4-3i) by an . appropriate factor to a give a product that is entirely real. What is the…

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Q: You should enter the coefficients of the powers of x of the sum in the boxes. 7(-2x? – 9x – 7) – 7…

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Q: x^3+ 3 x^2− 22 x −24 .  Hence,by use of long divison method ,find all remaining factors of the…

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Q: The polynomial 3x^4-2x^3+x^2-k is divisible by x+1. Find k.

A: Given:- p(x)= 3x4-2x3+x2-k, given polynomial p(x) divisible by x+1 To find:- value of k

Q: Find the product. (x+7)(x- 7) O A. x +14x-49 O B. x2 -14 O C. x2 -49 O D. x2 - 14x- 49

A:

Q: Which of the following is the correct factorization of 27x3 - 1? O (3x - 1)(3x² + x + 1) O (3x +…

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Q: Find the product:  (7 - 3i)(-2 - 5i).

A:

Q: Find the remainder when f(x) = 4x³ – 20x – 50 is divided by x – 3. %3D O-98 O 46 O-74 -2

A:

Q: Use complex analysis to prove the formula 2n n 7 7n V 3 n=0

A: It is given that

Q: When fully multiplied out, what is the 8th term of (x-3y)¹2?

A:

Q: The coefficient of x in 9x +7

A: Given: We have to find the coefficient of x in 9x+7

Q: Show that x-1 is a factor of P(x)=x² − 6x² +11x-6 and hence, determine all factors.

A:

Q: Use the Binomial Theorem to simplify (x – 2)3 as a polynomial ax3 + bx? + cx + d.

A: