Which of the following statements is not true regarding the division of polynomials?       a)  Terms should be arranged in descending order of degree in both the divisor and the dividend.   b)  If the remainder of polynomial division is zero, both the divisor and the quotient are factors of the dividend.   c)  Polynomial division is very different than the way numbers are divided.   d)  A polynomial can only be divided by a polynomial of the same degree or less.

Q: The remainder theorem indicates that if a polynomial flx) is divided by x - c, then the remainder is

A: We have to fill in the blanks: The remainder theorem indicates that if a polynomial fx is divided by…

Q: If the result of a polynomial division is 2x3 - 4x2 - 5x + 23÷ x + 2 make at lease three definitive…

A: Ans

Q: Let's review our previous lesson on synthetic division, remainder theorem and factor theorem by…

A:

Q: 2. If the result of a polynomial division is 2x – 4x? – 5x + x+2 23 ,make at least three definitive…

A: Consider the given: If the result of the polynomial division is-2x3−4x2−5x+23x+2It means , The…

Q: Use the factor theorem and synthetic division to decide whether the second polynomail is a factor of…

A: Factor theorem: according to factor theorem if (x-a) is a fctor of f(x) then f(a) must be equal to…

Q: g9. Find the goD01, hent f remainer Using synthetic division. メー4 quotinent: remainder:

A: Consider  x4+x3-77x-13x-4

Q: 1. Show whether the given polynomials 1+4x + x², 2+ 5x + 3x2, 3x 5x, and 3+ 15x - 8x spans p,.…

A:

Q: Prove that for any integer a, 9/(a - 3

A: To prove  For any integer a, 9 does not divide a2-9 By using the principle of contradiction.

Q: The remainder upon the division of x75 + 6 by x – 3 in z, is: O 1 O 5 O 6

A: Objective is to find the reminder.

Q: 2. If the result of a polynomial division is 2x³ – 4x² – 5x + 23 make at least three x + 2'…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Show that (2x+7) is a factor 2x2+5x2-11x-14.Hence factories the given expression completly ,by using…

A:

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: Determine whether the polynomials 1+7x, 5+x, x−2x2, 1+16x−6x2 +2x3 form a spannig set of P3. Explain…

A:

Q: What is true about the degree of the sum and difference of the polynomials 3x5y - 2x3y4 and - 8x5y +…

A: 3x5y - 2x3y4 and - 8x5y + 2x3y4 + xy3

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: 4. Find the factors of the following polynomials with complete solution using synthetic division.

A:

Q: In the given question , determine whether the statement is true or false. If it is false, explain…

A: fx=4x+32x-1 calculate the values of f(x) for given values of x x 100 101 102 103 104 105 106…

Q: Find the polynomials connecting the points (0,1), (1,3), and (2,13) ​​by quadratic interpolation.

A:

Q: Calculate the values of a, b, c in the polynomial p (x) = x³ + ax² + bx + c, knowing that it is…

A: ***I have to to find a, b, c from three simultaneous linear Equations.We can use row echelon form to…

Q: Determine whether the following polynomials span P2. P1 = 2-x+ 4x2, p2 = 4+ x, p3 = 24 + 3x + 8x2,…

A: Given :- p1 = 4x2-x+2 p2 = 0x2+x+4p3 = 8x2+3x+24 p4 = 8x2-4x-4 We can write the coeficient matrix…

Q: 8. Verify that (x2 - 1) + is a valid result for the x4 +3x2+4 polynomial long-division calculation…

A: Given : The divide the  polynomial x 6 + 2x4 + 2x2 - 4 by the polynomial  x4 + 3x2 + 4 . Result : x2…

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

A:

Q: The remainder upon the division of x8 + 4 by x – 4 in Z, is= None

A: Given: The given polynomial is x98+4 by x-4

Q: 3. Write down the polynomial having coordinates in B and the one with the same coordinates in B'.

A:

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: In the polynomial x^6 − 3x^5 − 5x^4 + 22x^3 − 39x^2 − 39x + 135, it is known that 1 + 2i and √3 are…

A:

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

A:

Q: A local city wants to compare the number of those with a car and those without a car, represented by…

A: Given,          A local city wants to compare the number of those with a car and those without a…

Q: 1.  if the result of a polynomial division is 2x3 - 4x2 - 5x +23/x+2,   make at least three…

A: Given that the result of a polynomial division is 2x3-4x2-5x+23x+2. It is required to make at least…

Q: The remainder upon the division of x98 +4 by x - 2 in z, is:

A: We have to use remainder theorem.

Q: Determine the remainder of 2 ^ 217 + 1 by division by 19.

A: To determine : The remainder when 2217  + 1  is divisible by 19.

Q: Use the factor theorem and synthetic division to decide whether the second polynomail is a factor of…

A: Given,

Q: The remainder upon the division of x98 +4 by x - 2 in z, is: 6. None

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: Which of the following operations on polynomials will always result in another polynomial? Select…

A:

Q: #9. USE SYNTHETIC DIVISION TO FIND THE QUOTIENT AND REMAINDER а. x – 8x – 5; x + 3 - 3x + 1; - 8 -…

A:

Q: For a fifth order polynomial, if r = a + bi is a root, and r = c+ di is a root, how many real roots…

A:

Q: if the result of a polynomial division is 2x3 - 4x2 - 5x +  23/ x +2 make at least three definitivve…

A: Given that the result of a polynomial division is 2x3 - 4x2 - 5x +  23/ x +2. Here, Divisor = x +2…

Q: If the result of a polynomial division is  2x^3-4x^2-5x+23/X+2 make at least three definitive…

A: Given result of the polynomial is- 2x3-4x2-5x+23x+2 Here, Quotient = 2x3-4x2-5x Remainder = 23…

Q: Use synthetic division and the Remainder Theorem to evaluate P(c). P(x) = 4x + 11 - Ex + 4, c= 1…

A:

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

A:

Q: 4. Use what you have learned about the Remainder Theorem to show that X +1 is a factor of 19x42 +…

A: We will use the remainder theorem that states that the remainder is zero when we decide the function…

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: Use short division to find the quotient and remainder for the division problem given below. 7)4859…

A:

Q: 23 2. If the result of a polynomial division is 2x³ –- 4x² – 5x + x + 2 make at least three…

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other…

Q: 2. If the result of a polynomial division is 2x3 – 4x? – 5x + 23 ,make at least three x+ 2…

A: The given result of a polynomial division is 2x3-4x2-5x+23x+2. Observe the following. Quotient,…

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

A: Answer

Q: Prove that 2r +1 is not a factor of 4r +r - 1.

A: We have to prove that  2x+1 is not a factor of  4x3+x-1.

Q: If the polynomials f1 and f2 are not divisible by the polynomial g, can their sum f1 + f2 be…

A:

Q: It can be proven that the expression (a +b) a - ab +b-) is equivalent to which of the following…

A: Given,            a + b a2 -ab + b2

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.