x) = 5x4 + 3x3 + 1 and g(x) =3x2 + 2x + 1 in Z7[x].  Determine the quotient and the remainder upon dividing f(x) by g(x). It needs to be applied to Z7.  My guess is we need to use mod 7 with the quotient and the remainder? I got (5/3)x2 - (1/9)x - (13/27) as the quotient. (29/27)x + (40/27) as the remainder.  This is not the correct answer as it states in the back of the book.  The back of the book has the following: Quotient:  4x2 + 3x + 6 and remainder 6x + 2

Q: 4. Show steps and find -9x²-9x-4 x³ - x 3 √⁹x² - dx. 3

A:

Q: 3. Express the following in simplest form with positive rational exponents only. a. 144x yz* (81a…

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: Three rational expressions have the following characteristics: a) Rational Expression 1 i. NPV's=…

A: Given that  a) NPV's are 52 and -5 and numerator is a difference of squares polynomial. b) NPV's are…

Q: 6. Which of the following could be used to perform the synthetic division for ( 3 + x3 + 6x4 - 7x)…

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Let f(x)=4x4+x3+x+1 and g(x)=3x2+2x+3 be two polynomials in Z5[x].  Determine the quotient and…

A:

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: Multiply and simplify. X- 1 x2 - 1 x2 +2x +1 X +1

A:

Q: When pr – 32x2 – divided by (2x + 3). Find the value of p 10x +r is divided by (x- 2), the remainder…

A:

Q: 9. Divide the polynomial 2r – 5x² – 4x + 3 by r +1 using synthetic division. What is the quotient?

A:

Q: Use synthetic division to show that f(x) = x³ + 3x² – 13x – 15 is divisible by the linear factor x +…

A: Given query is to use synthetic division on f(x) , and find its factors.

Q: Completly factorize x5 + 4x4 + 7x³ + 8x² + 4x + 2 in Q[x]. Justify that the found factors are…

A:

Q: QUESTION 2 2.1. Find the value of -3x²+ 8x-15 if x = -2. 2.2. (a) Add the following polynomials:…

A: Step 1: Step 2: Step 3: Step 4:

Q: Determine Q(x) when P(x)=x³-5x2-3x+2 is divided by x-1 and then expressed in the form Select one: O…

A:

Q: Which of the following are rational expressions? Vx + I (b) 2x + 3 x (x² – 1) 3x (a) x - 1 (c) x + 3

A:

Q: 1. [K2] Without dividing, determine the remainder when P(x) = 10x3 – 9x2 – 8x + 11 is divided by 5x…

A: We use remainder theorem for calculating the remainder.

Q: 3. Divide f(x)= x³ + 2x² - 2x+4 By (x-2) using synthetic division. What is the remainder?

A:

Q: 8.Differentiate the following. Do Not Simplify. 6x-x² a) y=√√5x²-3x(5-4x)³ b) y=√1-3x c) y = (x¹ -…

A:

Q: Find the factors of the following polynomials. 9. x? – 4 10. x2 + 4x-5 11. 3x + 6x² + 5x + 10

A: It is reuquired to find the factors of the given polynomials.

Q: I. Divide the polynomials using the LONG METHOD. Express your answer as P(x) = D(x) Q(x) + R (x3 –…

A: topic - long division method note : as per bartleby guidelines, we are supposed to answer only first…

Q: 5. Consider the following division: (2,3 – 4x² + x – 2) ÷ (x – 2) 5a Fill in the gaps to complete…

A:

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

A: Given expression is,

Q: 2) When a polynomial, ax-3x² - bx - 5 is divided by the binomial (x-3), the remainder is 10. When…

A:

Q: 7. For what value of b will the polynomial f(x) = -23 + b? remainder when divided byr-2 and r+1. 5x…

A: