9. When the polynomial mx' – 3x² + nx +4 is divided by x - 3, the remainder is 16. When it is divided by x + 2, the remainder is -14. Determine the values of m and n. Show your work algebraically

Q: If x4 −2x3 −12x2 +10x+ 3 = 0 has the roots 1 and −3,

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Q: Make up two polynomials, not of the same degree, with thefollowing characteristics: crosses the…

A: Here it is given that Polynomial  crosses the x-axis at - 2  touchesthe x-axis at 1, and is above…

Q: The number of zeros of the polynomial x² + 4x +1 in Z, is: 4 2 None

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Q: Verify the factorization by using synthetic division 3x3 - 5a2-4x + 4 = 3(x+ 1)(x– 2)(x –) Verify…

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Q: 1. When the polynomial 6x -ar' + bx² +3x+4 is divided by x+1 the remainder is 10. When it's divided…

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Q: To divide x^3+5x^2-2x+8 by x-5 using synthetic division,the first step is to write

A: According to question we have to calculate x3+5x2-2x+8x-5 By synthetic division

Q: Find the polynomial of the lowest possible degree which assumes the values 3, 12, 15, 21 when x has.…

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Q: Determine all the roots the following polynomial 24 – 2z3 + 10z² – 18z + 9 if one of the root is -j3

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Q: 1. When the polynomial f(x)= px' +5x +qx-2 where p and q are constants is divided by 2x +3x-2 the…

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Q: If a third degree polynomial has a lone x-intercept at x a , discuss what this implies about the…

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Q: Suppose you were asked to solve the following two problems on a test. (a) Find the remainder when…

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Q: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

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Q: When dividing x^3+2x+4 by 3x+2 in Z5[x], the remainder is None of the choices 2

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Q: 2. If the polynomial f (x) divided by (x – 3) gives a remainder of -1, then the remainder of…

A: Solution is given below:

Q: 15. If the zeros of the polynomial x²+px +q are double in value to the zeros of 2x²- 5x -3, find p…

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Q: 19) Determine a polynomial that represents the area of a square having sides of length s x + 8. B)…

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Q: Express the polynomial x5 + 3x3 + x2 + 2x as a product of its irreducible factors in Z5[x].

A: Given: [May be the question is wrong, otherwise the given solution is correct.] The given polynomial…

Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: Now let's attempt to work a similar problem backwards. Suppose you have a polynomial with leading…

A: Given  Leading coefficient =12 constant=15

Q: 7. What is the constant term of the polynomial expression: x* – 2x + x² – 5x + 6? А. 1 8. Express:…

A: Let's find.

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: Select the factors that multiply to create a polynomial with this description: (1) As x→-0, y→-∞ (2)…

A: Given x→-∞ and y→-∞ and x→∞ and y→∞ and x=4 is a root

Q: 5) If the leading term of a polynomial is -2x18, what do you know about the end behavior? As x → 0…

A: We will find the end behavior of the polynomial when Leading term is given.

Q: 4.9 (a) Evaluate the polynomial y = x – 7x + 8x – 0.35 | at x = 1.37. Use 3-digit arithmetic with…

A: Answer for sub question a: First determine the powers of x needed for evaluating the polynomial.…

Q: 9. Find the quotient and the remainder of x³ + 2x² – 1 divided by 3x2 +1 in Z7[x].

A: Note that for Z_7  Any number is equal to the remainder when it is divided by 7.

Q: 1. It is known that the polynomial p(x) = 2 – (x + 1) + x(x + 1) – 2æ(x + 1)(x – 1) interpolates the…

A: Solution by using Newton's forward difference interpolation method .

Q: To show that x = -3 is a solution of the given equation, divide f(x) = x -37x - 84 by (x + 3) using…

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Q: Then by using "Newton's interpolating polynomial method", the scientist got the following polynomial…

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Q: Suppose a polynomial of degree 4 with rational coefficients has the given numbers as zeros. Find the…

A: Surd zeros are always in pairs. That is a+b is zero then a-b is also a zero of the polynomial.…

Q: (a) What is the degree of Q(7, V3) over Q ? Justify your answer. Is the polynomial X - 5 € QIX)…

A: Degree of extension- Let E be an extension field of a field F i.e. F is a subfield of E, also E is a…

Q: 4. When the polynomial P(x) is divided by (x-2)2 the remainder is 3x - 3. What is the remainder when…

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Q: Is x+ 4 a factor of f(x) = x5 + 10x4 + 29x3 – 28x2 (Use Synthetic Division in conjunction with the…

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Q: The polynomial p(x) has the rest (x+2) when dividing it by (x^2+2x-3) and the rest 1 when dividing…

A: We have given that  p(x) leaves the remainder (x+2) when divided by x2+2x-3 and  p(x) leaves the…

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: what could be a polynomial with a degree of 5 if its zeros are -2,1, and 4?

A: The given zeros are, –2, 1 and 4.

Q: Which polynomial would have the following end behavior? x+ -00, f(x) - -00 x+ 0o, f(x) → -00 A y =…

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Q: The polynomial f (x) leaves the remainder x + 2 at the division with x ^ 2 + 2x-3 and leaves the…

A: Use the remainder theorem for the polynomials to determine the remainder when f(x) is divided by…

Q: 42. What is the polynomial equation whose roots are {-2, 2, and 4 of multiplicity 2} A. 2x* - 2x +…

A: As per bartleby guidelines we only give first question answers.

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

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Q: #7: For what value of k will the polynomial function f(x)=x'+6x² +kx=4 have the same remainder when…

A: The Polynomial Remainder theorem states that if x-b divides the polynomial, Qx, then the remainder…

Q: When px3 3 32x 2 − 10x + r is divided by (x x 2), the remainder is exactly the same as when it is…

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Q: 29. Select the quadratic polynomial with roots –1 and 4. x2 + 3x – 4 x3 – 2x2 – 7x – 4 4x² + 8x + 4…

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Q: 7. Find all the zeros of the polynomial: y = 2x* – 5x³ + 10x – 12. - -

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Q: 3. Do you agree with the statement that “ cubic functions must have at least 1 x-intercept but not…

A: Given:  To show “ cubic functions must have at least 1 x-intercept but not more than 3". To prove…

Q: If x = -1 is a root of the polynomial 0 = æ³ + 2x2 – 5z – 6. what are the other roots? Ox =-3, x = 2…

A: see next step

Q: We can apply Eisenstein criterion for irreducibility of the polynomial 4x10−9x3+24x−18 over Q. true…

A: Using Eisenstein Criterion for irreducibility of f(x) over Q,

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

A: The result of the polynomial division is, 2x3-4x2-5x+23x+2 Let, f(x)=2x3-4x2-5x+23x+2…

Q: what is a polynomial of the degree 4 with the interger coefficients with zeros of 1+3i and 2 (with 2…

A: we are given zeros as

Q: The value of f(3) for the polynomial f(x)=x3+x2-5x+3 is 24. What does this mean in terms of…

A: Given:  f(x) = x3+x2-5x+3 Now we have f(3) = 24

Q: 17) Perform the following division of polynomials by synthetic division. (x* – x³ – 9x² + 29x – 30)…

A: Given (x4-x3-9x2+29x-30) ÷ x2-3x+4