2. For what values of b will the polynomial ƒ (x) =-2x + bx² – 5x +2 have the same remainder when divided by (x – 2) and (x + 1). [4]

Q: if xo = 2, x1 = 3 and x2 = 4 the second degree polynomial for f(x) = using Lagrange Interpolation is

A:

Q: Find a, b, c E R such that the polynomial f(x) = x³ + ax? + bx + c is divisible by g1(x) = x + 2 and…

A: The remainder theorem says that when a polynomial px is divided by x-a. The remainder is obtained as…

Q: For what values of the constants A and B is the polynomial function Ax 2. 2 4 f(x, у) %3D Ах + Bxy +…

A:

Q: If a polynomial f(x) when divided by (x – a) gives a remainder r1, and when divided by ( – b) gives…

A:

Q: Find the nth Maclaurin polynomial for the function. 4x - 1 f(x) = n = 4 P4(x) =

A:

Q: 1. If the leading coefficient of an odd-degree polynomial function is negative, then the function…

A: Check the end behaviour of the function as x tending to minus infinity and infinity.

Q: For the polynomial f (x) = x³ – 2x² – 5x + 6 what is the end behavior as x → +∞ O x → ±∞ O x → -∞ x…

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Q: Find a, b, c E R such that the polynomial f(x) = x³ + ax? + bx + c is divisible by g1 (x) = x + 2…

A: The given question is related with polynomials. Given that,                  fx = x3 + ax2 + bx + c…

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

A:

Q: 4) For the function 16 4 y=-0.0519x+1.0777x-7.4569x +20.247x- 12.333 P=0.6113 12 10 4. 2. 4. time 10…

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Q: Factor f(x)=2x^3+5x^2-83x+40 into linear fuctors given that -8 is a zero of f(x)…

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Q: What is the lower bound of the polynomial function? f(z) = 1 - 4z - 9z2 +z – 16

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Q: Solve the problem. 13) Which of the following polynomial functions might have the graph shown in the…

A: Here we have to find the function.

Q: 3. If any of the linear factors of a polynomial function are squared, then which of the following is…

A: In this question, we have to find the correct option for the given statement as If any of the linear…

Q: If the result of a polynomial division is 2x 3 − 4x 2 − 5x + 23 x + 2 , make at least three…

A:

Q: For the given polynomial y a2x2 + azx³, determine a2 and az that will make %3D (1,3) a point of…

A: Based on trial and error method we will solve the the first equation.  As per the bartleby policy,…

Q: Find the critical points, A and B, of the following polynomial (with A < B). f(x) = 4x° – 588x – 6 -…

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Q: 4. The possible equation of polynomial function for the following graph is a) f(x) - (х-2)(х+3)(x-5)…

A: Graph of the polynomial function is given, we have to find its equation. Note: Multiple questions…

Q: - Given that ( x + 1) is factor of the polynomial P(x) = x³ – x² – x – m. The value of m is A 1 B в…

A: Using polynomial and its factor properties

Q: 1. Determine the coordinates of the vertex of each of the following using the method given. a) f (x)…

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Q: 8. The graph that could represent a fifth degree polynomial of the form y = ax+ bx + cx + dx² + ex +…

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Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) = n = 4 x + 1 P4(x) =

A: A Maclaurin polynomial of nth order  for the function f(x) is               f(x) = ∑n=0∞fn(0)n!xn,…

Q: The ________ Theorem states that if a polynomial f(x) is divided by x − k, then the remainder is r =…

A: The ________ Theorem states that if a polynomial f(x) is divided by x − k, then the remainder is r =…

Q: Find the zero/s of the given polynomial function f(x) = x* + x³ – 29x2 – 9x + 180

A: The factors of a quadratic form of equation ax2+bx+c can be calculated using integer factorization .…

Q: If x* – 1 = (x – 1) q (x), which polynomial represents q(x)? |

A: As we know that (x2-y2)=(x-y)(x+y)

Q: Factor f(x) = 2x + 9x- 33x + 14 into linear factors given that -7 is a zero of f(x). f(x) = 2x°…

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Q: For f(x)=2x4 +2x3-1 and g(x)=2x3 +2x+3 in Z4[x], the degree of fg is 7. True or false

A:

Q: Express the polynomial x3 + 2x + 3 EZŞ[x]as a product of irreducible polynomials of Z5[x].

A: Explanation of the answer is as follows

Q: Find the roots of the quadratic polynomials:(a) f (x) = 4x 2 - 3x - 1 (b) f (x) = x 2 - 2x - 1

A: We set them equal to 0 and solve for x we first factor the left side then we set each factor equal…

Q: Suppose the coefficients of the cubic polynomial p(x) = a +bx+cx^2+dx^3 satisfy the equation:…

A:

Q: Which polynomial function has 3 as a zero of multiplicity 4 and − 6 as a zero of multiplicity 2?…

A: Total number of repetition of a single zeroes in a function is called it's multiplicity: Since given…

Q: (1) As x→ t0, the end behavior of the polynomial p(x) = 3x°(1 – 2x + x°) can be resembled as (A)…

A:

Q: 10) If x = 1 is a zero, what are the other zeros for x3 - 3x2 + x + 1 = 0 ?

A:

Q: Given that the interpolation error is E, (x – x1)(x – x2) ...· (x – xn). (n+1)! Why is the error…

A: We have the interpolation error is En=fn+1ξ(n+1)!x-x1x-x2...x-xn Now, the roots of the Chebyshev…

Q: 3- Determine the Lagrange polynomial that interpolates the data in the following table 2 4 y 1 -1 3…

A: From the given information, x0=0,x1=2,x2=4,x3=6 and y0=1,y1=-1,y2=3,y3=4. Formula for Lagrange's…

Q: Find the nth Maclaurin 3x - 5 f(x) = x + 1 P4(x) = polynomial for the function. n = 4

A: Given function f(x) =3x-5x+1

Q: 4. Use synthetic division to show that c is a zero of the given polynomial function. b. P(x) =2x³ –…

A: Solution is given below:

Q: If we divide the polynomial P by the factor x - c and we obtain the equation P(x) = (x – c)Q(x) +…

A: we know that if we divide the polynomial px by the factor x-c and we obtain the equation…

Q: Which polynomial function has 1 − 3 i and 4 i as zeros? Group of answer choices f ( x ) = x 4 − 6 x…

A: The given zeroes are 1-3i and 4iwe have to find the polynomial function which has zeroes

Q: Given that the degree of the polynomial f(x) is 8, which of the following most accurately describes…

A:

Q: if xo = 2, x1 = 3 and x2 = 4 the second degree %3| polynomial for f(x) = using Lagrange…

A: Given function is f(x)=12and the nodes are x0=2, x1=3 and x2=4. We have to find second degree…

Q: Find the critical points, A and B, of the following polynomial (with A < B). f(x) = 2x³ + 3x² 336х —…

A: Given polynomial function

Q: Which of the following polynomial functions has the roots 3, -1, 1, 4?   a. P(x)= x4 - x3 + 13x2 -…

A: The general form of a polynomial equation of degree n is given by a0xn+a1x1....+an-1x+an=0. The root…

Q: Find the critical points, A and B, of the following polynomial (with A&lt;B). f(x)=2x^3−24x^2+5 A=B=

A:

Q: Given that 5x - 2is a factor of polynomial functions f(x) kx- bx + 2k, %3D determine the ratio k: b…

A: Given that 5x-2 is a factor of polynomial functions f(x)=kx2-bx+2k.

Q: there is at most one polynomial of degree less than or equal to n_____ option,(a) which interpolated…

A: Using interpolation theory, We need to check which option is correct.

Q: Find the nth Maclaurin polynomial for the function. 5x - 4 f(x): n = 4 x +1 P4(x) =

A:

Q: It is known that (x + 2) is a factor of the polynomial P(x) and that P(x)= (xtxt )X Q(x)+ (2xt3).…

A: We will find out the required value.

Q: Find the nth Maclaurin polynomial for the function. 4x - 5 f(x) n = 4 x + 1 P4(x) = =

A: The function is  f(x)=4x-5x+1