2n b) The polynomial, fW =2x" +mx-3, where m and n are real constants, %3D is divisible by (x+1) but leaver a Feminder remainder of 156 when divided by (X-3). Find the values of n and m.

Q: Consider two nonnegative numbers x and y such that x+y=3. What is the difference between the maximum…

A: Given: The given equation is x+y=3, where x,y are non-negative numbers. To find: The main aim is to…

Q: For n = 4 , Legendre polynomial is 94 (x) = (35x – 30a? + 3)/8 %3D Find all its four roots.

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Q: b) When x + x* – 2x? + k is divided by 1 + x², the remainder is 5. Find the value of k. -

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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: (b) Generalize the remainder theorem to work for lm.d if m 7 0 instead of only l1,-k. In other…

A: b) We want to find the remainder after dividing f by lm,d if m≠0. Where f is a polynomial and lm,d…

Q: What is the value of k so that (x3 +4x 2+x + k)÷(x+2) give a remainder of 3?

A: To find the value of k so that x3+4x2+x+k÷(x+2) gives a remainder 3.

Q: . Find a general solution for y" + 4y = x² by method of undetermined coefficient

A:

Q: 8) Is (x+3) a factor of x4 + 2x2 + 17x – 48 Drop coefficients onto top line

A: Given,  x4+2x2+17x-48

Q: 3.  How many possible rational roots are there for the polynomial P(x) = 10x^3 + 6x^2 +4x+4? A.) 10…

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Q: 2- M ke 2.

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Q: What is the quotient and remainder after dividing the following: f (x) = 2x3 18x? – 16x 50 by x- 10…

A: Solution

Q: 9. When the polynomial mx' – 3x² + nx +4 is divided by x - 3, the remainder is 16. When it is…

A:

Q: Compute A−2 two different ways and show that the results are equal.

A: Given: To Find: A−2 two different ways and show that the results are equal.

Q: find the quotient and remainder f (x)=x4+x2+6x-10 is divided by x+2

A: Given function is Divisor is

Q: 10. Use the appropriate method to solve the following polynomials. a. y = x* + 35x² – 36 - b. y =…

A:

Q: oan What is the result when 2x + 13x2 + 15x 15 is divided by x +3? If there is a r(x) . (2)q…

A:

Q: 14 5x - 21 16 2r + 3

A: When two triangles are similar then their side ratios are proportional.  So we get relation  MPQP=…

Q: 2. For what values of b will the polynomial ƒ (x) =-2x + bx² – 5x +2 have the same remainder when…

A:

Q: What is the largest number k for which 2x+3y=20 and 3x+4y=k have the same number if positive integer…

A: Given that, there are two equations following, 2x + 3y = 20…

Q: 3. What is the number of coefficients of a polynomial of degree n in two variables? In three…

A: Given: A polynomial of degree n.

Q: What is the largest number k for which 2x + 3y = 20 and 3x + 4y = k have the same number of positive…

A: Given: 2x+3y=20...............eq(1) 3x+4y=k..................eq(2)   To find:What is the largest…

Q: 9. When -6x - 7x + qx- 12 is divided by 3x - 4, the remainder is 0. Find the val

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Q: the area of the region enclosed by 4x−y−16=0 and y2−4x=4.

A:

Q: 8. The polynomial 3x³ + mx² - nx – 10 has a factor of x - 1. When divided by x + 2, the remainder is…

A: P(x) = 3x3 + mx2 - nx - 10                (i) It is given that (x - 1) is a factor of the above…

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: Suppose XY is congruent to YZ. If XY is 8x + 8 and YZ = 2x + 18 what is the value of x? If needed,…

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: 22) Find m2TSR R U 2x + 14 2x – 7 125° - S

A:

Q: Determine the values of m and n for f(x)=mx3+20x2+nx-35 given that (x+1) gives a remainder of zero,…

A: Given that f(x)=mx3+20x2+nx-35 given that (x+1) gives a remainder of zero, and when divided by (x-2)…

Q: Find the value of k so that the remainder is 4 when x – kx² + 2x – 8 | is divided by x + 3.

A: According to reminder theorem, if a polynomial p(x) is divided by the binomial (x—a) then the…

Q: 10. When dividing x* + 3x? + 2x + 1 by x² + 2x + 3 in Z5[x], the remainder is а) 0 b) 2 c) 3 d) 4 a)…

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Q: nte poirts 2. 5) and (-3 -4) has an eguaton of 9x + 5y =0 9x +5y-7-에

A: Solution

Q: 26. What is the remainder when f(x) = x³ - 7x+ 8 divided by x + 1? A. 14 В. З С. -1 D. 5

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Q: When p (x)=2x + kx +1 is divided by x +1, the remainder 1s the same as when q (x)=3x + kx +2 is…

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Q: Find m so that x+4 is a factor of 5x^3 + 18x^2 + mx + 16 i need a detailed explanation, please.

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Q: 1. Find the first-order derives: III. y = (2x* – 5)(3x5 + 12) IV. V4x? + 7+ 5-x° + 15x – 30 5x+ 4x3

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Q: While reducing the fraction 200..0z 300...0y (x, y + 0) in which between 2 and a and between 3 and y…

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Q: Show that for r=1x1 XER³, > A( 7 ) = 0 we have when 1x1=1 #0

A: Laplacian operator

Q: Find the value of the constant "k": 3x^2-5x+ 4k-5-0 has one root equal to 0.

A: We will use formula for root of quadratic equation

Q: 24 Use the diagram to solve for x, FG and FH. 4x 7x +6 FG = FH = 6 8 9 DELL -> 23 $ & 3 4 7 8.

A:

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

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Q: Find all the solutions of z° . .. + 8° = 0 + 8z° + 8²z7 +

A: (z9+8z8+82z7+83z6+8 4z 5+8 5z 4+8 6z 3+8 7z2 +88 z1 +89)=0multiply by (z-8) on both…

Q: A polynomial f(x) = x³ + ax² – 3x + b when divided by 91 (x) = x – 2 gives a remainder of 6 and f(x)…

A: Given:             fx=x3+ax2-3x+b using remainder theorem: fx=x3+ax2-3x+b is divisible by g1x=x-2…

Q: 1. What must be multiplied to (x2 + 2x + 1) to get (x + x + x2 + 3x + 2)? С. -ха- х - 2 D. x2 - x +…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: 2). when 2x°-3x+Kx-1 is divided by X-1 the remainder is 2, find Ke

A: value of k is 4  see below the calculation and answer

Q: 6. Divide 6x + x² – 12x + 5 by 2x – 1. Is the divisor a f of the dividend?

A: In a division, divisor is said to be a factor of the dividend if dividend can be divided completely…

Q: ven the polynomial y = 29x – 10x? – 21, • list the possible rational roots:

A:

Q: The number of tickets sold each day for an upcoming performance of Handel's Messiah is given by N(x)…

A: We use second derivative test to find out number of days where tickets sell at peak

Q: Flx)=14x=2x - 2x find obliq-es asympto tes use the long Formula

A: