The polynomial R(x) is the remainder upon dividing x2007 by x-5x +6. If R(0) can be expressed as ab(a"- b°), find the value of -5x+6. If R(0) can ab(a - b), find the value of a +b +c=? 20

Q: Find the zeros of the polynomial f(x) = 3 its two zeros are equal in magnitude but opposite in sign…

A:

Q: Given that one of the zeroes of the cubic polynomial ax3+bx2+cx+d is zero , the product of the other…

A:

Q: What is the remainder when the polynomial f(x) = 4x* – 3x³ + x? + 10x – 1 is divided by (x- 2). %3D

A:

Q: Solve the problem. 11) Find a polynomial for the perimeter of the rectangle. (4x + 6) units - X +…

A: The perimeter is the length of the outline of a shape. To find the perimeter of a rectangle we have…

Q: If  x3 + 7x - a has a remainder of 1 when divided by x+1 then a has a value of __?

A: Please refer the attached image for complete solution.

Q: Find the condition which must be satisfied by the coefficients of the polynomial p(x)…

A:

Q: Use synthetic division to show that 5 is a solution of x4 - 4x3 - 9x2 + 16x + 20 = 0. Then solve the…

A: Coefficients of x4 - 4x3 - 9x2 + 16x + 20 are 1, -4, -9, 16, 20  Then we use the synthetic division.…

Q: If f(x) = 4x⁵ + 3,then what is the remainder when f(x) is divided by x - 2 ?

A:

Q: The polynomial 2x^3 + ax^2 - 10x + b has a factor of ( x-1 ) and has a remainder of 15 when divided…

A:

Q: 4. The polynomial equation whose roots are {-1, - ½ and 3} is А. 2х3- Зx2 - 8х-3%3D0 В. х3 - 6х2 - х…

A:

Q: Find a degree 3 polynomial that has zeros -4, 2 and 8 and in which the coefficient of x is-12.…

A:

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…

A:

Q: Find a polynomial (x) of degree 4 that has the following zeros. 7, -6, 0, -3 Leave your answer in…

A: Given Zeros of the 4th degree  polynomial are  7,-6, 0 and -3. Note: If a, b, c and d are the zeros…

Q: Use synthetic division to show that 5 is a solution of x* - 4x – 9x² + 16x + 20 = 0. Then solve the…

A: To show that 5 is a solution of, x4-4x3-9x2+16x+20=0

Q: What is the remainder when f(x) =x3 - 2x2 +4x -21 is divided by x - 3? Is x - 3 a factor of f(x)?

A:

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

A: Given function is Divisor is

Q: The polynomial -6x + 50x+ ax+ 24 has factors x-1 and 2x + 1. Determine the value of a.

A: Suppose px be the given polynomial such that px=-6x3+50x2+ax+24 And the factors of the polynomial…

Q: If the remainder on dividing the polynomial 2x* – kx +5x-3k+3 by (x + 2) is 4, then find the value…

A: Use the given information.

Q: Solve the polynomial 5x* - 16 + 3x2 + 20x - 4 = 0, given that 2 is a root of multiplicity 2.

A: Given polynomial is : 5x4-16x3+3x2+20x-4 = 0 The root x=2 has multiplicity 2.

Q: The value of r for which x2 - rx - 2 and x3 + x2 - x - 1 have a common factor is?

A: Given two equations x2-rx-2=0 and x3+x2-x-1=0

Q: Find a polynomial / (x) of degree 4 that has the following zeros. 0, -8, 9, -5 Leave your answer in…

A: Given data: The first zero of the polynomial is x1=0. The second zero of the polynomial is x2=-8 The…

Q: Find the zeros of the polynomial f (x)=x3-5x2-16x+80  ,if it's two zeros are equals tin magnitude…

A: The no. of roots of a polynomial is depend on the degree of polynomial Since, degree of this…

Q: We want to find the zeros of this polynomial: p(x) = 2x3 + 4x² – 6x

A: You will find the roots of the given polynomial by factorising

Q: Find the remainder if F(x)=6x^3+49x^2+90x+56 is divided by 3x-3

A: F(x)=6x3+49x2+90x+56 Since 3x-3 is linearwhere 3x-3=0⇒3x=3⇒x=1 Remainder of F(x) when divided by…

Q: Find a polynomial of lowest degree with rational coefficients and -4 and 5i as two of its zeros

A: Imaginary root always exist in pair form.

Q: Given the polynomial: f (x) = 2x° + mx* – 40x° + nx² + 218x – 168 And that two of the roots are x= 1…

A:

Q: How many zeros does the polynomial 3x2 + 2x + 1 have in Z6?  I thought it was three but that was…

A: Solution: Given Polynomial is  3x2+2x+1   over  ℤ6

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: When a polynomial, P(x), is divided by 2x - 1, the quotient is x2 - 8x + 3 and the remainder is -12…

A:

Q: Find the quotient of the polynomials using LONG DIVISION. Show your solution. (2x4 - 9x3+ 9x2+ 5x…

A:

Q: Find the remainder when: 3x3-2x2-4x+1 is divided by (x-2); and (x +3) When 3x -2x-4x + 1 is divided…

A: remainder is (9) remainder is (- 86)

Q: Find the equation of the polynomial with roots √2 and -5i, real coefficients, and passing through…

A:

Q: The polynomial 3x2 + bx - 4 has x - a as a factor, where a #0. Express b in terms of a.

A: Given polynomial is 3x2+bx-4...........(1) (x-a) is a factor of (1), so plugging x=a in the given…

Q: The problem involve the Remainder Theorem.

A: Given, P(x)=x500+6x101-x2-2x+4 We know by remainder theorem ,if a Polynomial function P(x) is…

Q: The problem involve the Remainder Theorem.

A:

Q: Find the zeroes of the polynomial x2-3 and verify the relationship between the zeroes and the…

A:

Q: Find the quotient and the remainder when  2x^4+3x^3+x+1 is divided by 3x^2+1 in Z5[x].

A: We have to find the quotient and remainder when 2x4+3x3+x+1 is divided by 3x2+1 in ℤ5x

Q: Find the remainder when f(x) = 2x5 – 8x3 +3 is divided by 3x + 2. -

A: Long Division of Polynomials: A long division polynomial is an algorithm for dividing polynomial by…

Q: Find the value of the polynomial  5x-4x2+3 at x = 2 and x = -1

A: Given, F(x)= 5x-4x2+3 At x=2 F(2)= 5*2-4*22+3 F(2)= -3

Q: The polynomial 6x^3 + mx^2 + nx - 5 has a factor of x + 1. When divided by x - 1, the remainder is…

A:

Q: If f(x) = 4x2 + 5x +2, then what is the remainder when f(x) is divided by x +7? %3D

A:

Q: 3. If x=-2 is one of the roots of 6x'+11x - 4x -4 = 0, find the other two roots of the polynomial…

A:

Q: find the remainder when the polynomial x^4 - 6x^3 + 4x^2 + 5x +3 is divided by (x + 1)

A:

Q: 5. If the remainder dividing the polynomial P(x) = 2x³ + kx? + 7x +6 by x- 4 is 114, find the…

A: Quotient Remainder theorem  The answer after we divide one number by another. dividend ÷ divisor =…

Q: find the zeros of the polynomial f(x) =x3 -5x2 +16x+80,if it's two zeros are equal in magnitude but…

A: Given,           The polynomial is fx=x3-5x2-16x+80.

Q: If it is given that -5 is one of the roots of the polynomial z* + 9z3 + 21z² + pz – 130 = 0, find…

A:

Q: Use synthetic division to find the result when x + 2x2-11a + 24 is divided by x +5. If there is a…

A:

Polynomials

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