What is the remainder theorem and long division? Compare and contrast the usefulness of both.

Q: 2. Calculate (4x³ – 6x² – 14) (x + 6) using long division. Show your work! -

A: Perform long division method

Q: Use the Remainder Theorem to find the remainder. (3x3 + 4x2 – 8x + 2) ÷ (x – 3)

A: Given (3x3 + 4x2 – 8x + 2) ÷ (x – 3) Now we have to find remainder by using remainder theorem

Q: How can the Division Algorithm be used to check the quotient and remainder in a long division…

A: The polynomial division is checked by multiplying the divisor with the quotient and then we add the…

Q: you have learnt about the remainder theorem and long division. Compare and contrast the usefulness…

A: In this question we are given with two methods: Reminder theorem. Long division method.

Q: State the Remainder Theorem.

A: Statement: If f(x) is divided by (x-a) then the remainder will be f(a).

Q: use synthetic division to determine the quotient and remainder. (3x4 - x3 + 2x2 - 7x - 1) ÷ (x + 1)

A: Given that 3x4-x3+2x2-7x-1÷x+1. Apply the synthetic division as follows. 3-1 2-7    -10-3 4-6    133…

Q: Use the Remainder Theorem to completely factor p(x) = x3 - 6x2 + 11x - 6.   please explain this…

A: Given: px=x3-6x2+11x-6 For doing factors of given expression, we first use hint and trial method So,…

Q: What is the remainder when f(x)=x3−22x2−16x−161f(x)=x3−22x2−16x−161 is divided by (x−33)(x−33)?

A:

Q: How can you determine whether a linear binomial is a factor of a polynomial without using the…

A: to find : How can you determine whether a linear binomial is a factor of a polynomial without using…

Q: Without actual division,Find the remainder obtained on dividing (3x2+5x-9) by (3x+2)

A: Given:                   3x2+5x-9   On dividing by :                   (3x+2):   Solution:…

Q: Create your own division problem and show how to use the Remainder Theorem to determine whether a…

A: A binomial is a factor of a polynomial function if and only if when it is divided the polynomial…

Q: Without actual division , find the remainder obtained on dividing (3x² + 5x – 9) by (3x +2)

A:

Q: Explain how the Remainder Theorem can be used to find fl-6) if f(x) = x* + 7x + &r? + 11x + 5. What…

A: The remainder theorem states that when a polynomial f(x) is divided by a linear polynomial  x-a, the…

Q: 8x4–16x3+9x² – 6x+4 y = 2x3+5

A: using long polynomial division method to solve

Q: If the result of a polynomial division is 2x 3 − 4x 2 − 5x + 23/ x + 2 , make (explain in detail) at…

A: If the result of a polynomial division is 2x 3 − 4x 2 − 5x + 23/ x + 2 .  To find: Explain at least…

Q: True or False: Synthetic division is a process of dividing a polynomial by a binomial and analyzing…

A: Synthetic division is a process of dividing a polynomial by a binomial and analyzing the remainder.

Q: Use synthetic division and the Remainder Theorem to evaluate P(c). P(x) = 6x5 + 10x3 + x + 1,  c =…

A: Px=6x5+10x3+x+1  ,  c=-2

Q: Consider the following Polynomial Division: (3 x3 + (-8)x2 + (-9)x + 5) (x+2) What is the remainder…

A:

Q: Use the Remainder Theorem to show that X+1 is a factor of 19x42 + 18x -1.

A: we have to divide the equation 19x42 + 18x -1 by x+1 by remainder theorem so, for that we will first…

Q: The remainder upon the division of x75+ 6 by x-3 in z, is: 5 6.

A: The remainder upon the division of x75+6 by x-3 in ℤ7is determined as shown below

Q: Explain how the Remainder Theorem can be used to find f(-6) if f(x) = x4 + 7x3 + 8x2 + 11x + 5. What…

A: Given that, f(x)=x4+7x3+8x2+11x+5

Q: What does it mean to have a remainder of 0? This pertains to Division with Polynomials.

A:

Q: How is the Remainder theorem and Long Division Theorem compared? What is the contrast between…

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Q: What does the remainder theorem tell us?

A:

Q: Does is verify the results of the long division process shown below? 2x + x+ 18 x+ 2)2x – 3x2 + 4x +…

A: Verifying the long division process.

Q: Use synthetic division and the Remainder Theorem to evaluate P(c). P(x) = 6x2 + 3x + 9, c=- Need…

A:

Q: Consider the following long division problem: (6x - 4 + 2x3) ÷  (x+4)We begin the division process…

A: Given  (6x - 4 + 2x3) ÷  (x+4)

Q: what is the remainder in the polynomial 2x^4-5x^3+12x-7 divided by x-1

A: Perform the division:

Q: Find the quotient and remainder using long division. −x^3+3x^2−6x−10  over x^2−x−3

A: By applying the polynomial long division method,

Q: 2. Use Synthetic Division to find the quotient and remainder: x³ – 6x² + 5x + 15 is divided by x + 1

A:

Q: compare and contrast the usefullness of remainder theorem and long division

A: The remainder theorem is used to divide two polynomials. The long division method is used to divide…

Q: When the following polynomial division is performed, what is the remainder? (4x – 3a2 – 4x + 1) ÷ (x…

A:

Q: theorem

A:

Q: Use synthetic division to divide x3−x2+xx3-x2+x by x−2x-2. Give your answer in the form…

A:

Q: Use synthetic division and the Remainder Theorem to evaluate P(c). P(x) = 4x2 + 12x + 5,  c = -1

A: We have been given the polynomial P(x) = 4x2 + 12x + 5 , c = -1

Q: Without actual division ,find the remainder obtained on dividing (3x2+5x-9) by (3x+2)

A: Find the solution below

Q: The problem involve the Remainder Theorem.

A:

Q: use long division and the remainder theorem to evaluate P(c). P(x)=x^3+2x^2-7,   c=-2

A:

Q: If the result of a polynomial division is 2x3 − 4x2 − 5x + ___23­­­­____…

A: Given that, the result of a polynomial division is 2x3−4x2−5x+23x+2. From the given information, it…

Q: In using the synthetic division method to divide (3x5 -2x4 + 2x2 -3x + 5) by (x+4), the order for…

A:

Q: Give a careful statement about the degree of the sum of two polynomials of the same degree.

A: The degree of the sum of two polynomials of same degree equals to the degree of one of the…

Q: What is the remainder when f(x) = x3 – 13x2 + 40x + 18 is divided by x – 7? Show your work.

A:

Q: How can i  use synthetic division to find the zeros of a 4th degree polynomial?

A: The solution for the above question is as shown below.

Q: If the result of a polynomial division is 2x - 4x2- 5x + 23 make at least three definitive x+2…

A: Answer

Q: 1. (x³ – 37x – 84) ÷ (x – 7) -

A:

Q: Use synthetic division to determine whether or not (x+5) is a factor of (4x3-10x2-8x+6) Quatient:…

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Q: Use synthetic division to divide x5−x4+x3−x2+x−6x5-x4+x3-x2+x-6 by x−1x-1 What is the quotient and…

A:

Q: Since your D2L says that synthetic division is a shorthand method for long division, why don't we…

A: Yes, the synthetic method is a shorthand method for long division.  But there is a constrain for…

Q: Use synthetic division and the Remainder Theorem to evaluate P(c). P(x) = 3x + 14x - 2x + 8, c = 5…

A: Given, P(x)= 3x³+14x²-2x+8 c= 5 We know that, Remainder Theorem states that, P(c)= P(x)/(x-c)