w that : The degree of Q(√√2, √√5) ove least 35. The degree of (√√2, V5) ove most 35. The polynomial x7 - 2 € irreducible over Q (V5).

Q: For a polynomial P(x), if P 0, then which of the following must be a factor of P(x)? %3D a) 5x +3 b)…

A: If a is zero of polynomial P(x)   i.e. P(a) = 0 then (x-a) is factor of polynomial.

Q: b) When x + x* – 2x? + k is divided by 1 + x², the remainder is 5. Find the value of k. -

A:

Q: when p = 60 dollars. 70. A manufacturer of the latest basketball shoes has found that the revenue…

A:

Q: 25. Use your work done in #24 to draw a rough sketch of f(x) = 4x4 + 8x³ + 19x² + 32x + 12.

A: 25. According to question,Given Function,fx = 4x4 + 8x3 + 19x2 + 32x +12

Q: 6) (s4 + 5s3 + 2s².17s+ 7) ÷ (s - 1)

A:

Q: 10. Find the principal root: (√15625r12g18) 2

A:

Q: 3. What polynomial, when divided by 2x, yields 6x° -5x* + 8x as a quotient? Let's try that again…

A:

Q: What is the value of k so that the polynomial P \ left (x \ right) = x ^ 5−23x ^ 4 + \ left (2k − 3…

A: Given : P(x)=x5−23x4+(2k−3)x3−17x2−54x+40 Q(x)=x-2 Remainder theorem states that x -a is the divisor…

Q: x)º. b is divided by x- - 1 the remainder is 1, but when it is is -1. If possible, find the values…

A:

Q: What is the degree of the polynomial 3x4-5x3+7x2-2x+8?

A: Degree of polynomial: The highest or the largest power of the variable denotes degree of variable…

Q: Q14: What is the coefficient of the term independent of x and y in the multinomial expansion 3 4 (5x…

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Q: 222-10x +r is devided by (xt2), the remaindler e same as when it is divided by lar+3). of to

A: The given question is solved below.

Q: What is the minimum number of multiplications that we need when we evaluate the following…

A: In order to get nth exponent of any number, minimum number of multiplications required will be…

Q: a) Function f(x) is defined as f(x) = 54x³ + 21x² - 23x - 10. When f(x) is divided by (3x - k), the…

A: To find the values of k using the Remainder Theorem, we need to equate the remainder when dividing…

Q: 11 When 2x' + x² – 2kx + f is divided by x – 1, the remainder is -4, and when it is divided by x +…

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Q: ils (factored form) We want to find the zeros of this polynomial: p(z) = (z+2)(2z - 3)(z-3) Plot all…

A: To find the zeros of the polynomial, equate the given polynomial to zero.

Q: Q: Let f (x)= x³ - 6x² - 4x + 24. a) Use grouping to factor completely the right hand side. List the…

A:

Q: A fourth degree polynomial expression is shown below. (x2 – 9x +20) (x²+ 4x-32) Which of the choices…

A: Given, (x2-9x+20)(x2+4x-32)

Q: What is the quotient if P(x)= x³ +4x ² + 3x -2 is divided by x-3 using the long method. * a. x ² +…

A: The detailed solution is given below Thank you

Q: K2. What is the remainder when x5+2x4 - 5x³ - 3x² + 4x - 10 is divided by (x+3)? W Ox4x³2x² + 3x - 5…

A:

Q: Use synthetic division method to find the quotient of each the following. Show the solution on the…

A: 1. (x3-3x2+5x+3)÷(x-3) Using synthetic division, The quotient is q(x)=x2+5. The remainder is…

Q: 1. Is x³ - 2√5x + x a polynomial? If not, state a reason. 2. Is -2020x a polynomial? If not,…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

Q: Q5: Find the residue of 8 1+5z2

A:

Q: L Find for the quotient of the following polynomials using long division. 1. (x - 6x + 8) + (x-2)

A: Perform a long division method

Q: What is the multiplicity of the root r = 2 for the polynomial y = x³ – 3? + 4? O 2 O 4 O 1

A: Given polynomial is, y=x3−3x2+4

Q: 5. (3x + x + 3x - 6) + (3x + 5) 6. (4x' + 3x - 3x - 5) + (4x-7)

A: Solve the above questions.

Q: \/(r2 – 6r + 9)    a. Defined for all reals.              b.      r 3   c. r -3…

A:

Q: The polynomial y = x³ + æ³ – a? – 1 factors into (x? + 1)(x³ – 1). What is the multiplicity of the…

A: Polynomial y = x5+x3-x2-1Factored form: x2+1x3-1Equate x3-1 = 0                +1     +1x3 = 1Taking…

Q: Determine the remainder using long division and show the complete solution. 1. (x³ + x - 22x - 25) +…

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Q: 1. [K5] Use long division to divide 4x* – 2x² - 1 by x – 1. Then write the associated division…

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Q: is -√5 rational or irrational

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Q: D. Using the remainder theorem, find the remainder when f(x) = x - 13x +12 is divided by: 16. x-3…

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Q: Find all zeros. f(r) = x* – 4x3 + 11x² – 14x – 30 %3| (a) 3) Find all possible rational zeros. (b)…

A: To find all possible zeroes, we will take all factors of p/q, where p represents the constant and q…

Q: Find f(x) and g(x) such that h(x) = (f o g)(x) and g(x)= 8-5x. h(x) = (8-5x) - 5(8-5x)2 +4(8-5x)-1…

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Q: 2. Which of the following list are the possible zeros of the polynomial function f(x) = 11x* – x² +…

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Q: 3 When x³-x+4 is divided by a polynomial f(x), the quotient and the remainder are +2x+3 and 10…

A: Topic:- algebra

Q: Detemine the x- values at which, g(x)= 2x-3x²+x 2x3+5x²-3x is undepined. Evaluate the limit ac x=8…

A: To find: The value of x at which g(x)=2x3-3x2+x2x3+5x2-3x is undefined also evaluate the limit as…

Q: When dividing the polynomial x³ + bx² + 2x +9 by x + 1, the remainder is 10.

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Q: 47. a) If (x – 2) is a factor of 2x – 3x + k, find k. - b) When ax – 4x² + 5x – 3 is divided by (x +…

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Q: Factor by removing the common monomial factor: 24x²y°z* + 8xy°z° O 8xy²z³ (3xyz + 1) 8xyz (3xy z+ y)…

A: