Let f(x) be a polynomial with real coefficients. The polynomial f(x) leaves the remainder 2x +1 when it is divided by 3x² + 1 and leaves the remainder 6x – 1 when it is divided by x² + 3. Find the remainder when f(x) is divided by 3x + 10x² + 3.

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

A: Given, Polynomial  =  5x- 4x2 + 3  Finding the value of polynomial at x = 2  = 5*2 - 4(2)2 + 3 = 10…

Q: Divide the polynomial f(x) = x³ + 4x2 + 5x + 2 by (x + 2) (x + 4x2 + 5x + 2) ÷(x + 2)

A: To divide the polynomial f(x) = x3 + 4x2 + 5x + 2 by x + 2

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Q: Find all real and imaginary zeros for the polynomial function f(x)=x3+8x2+24x+27.

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

A: Find the zeros of the polynomials f(x) =x2 -5x2 -16x +80 ,if it's two zeros are equal in magnitude…

Q: Given the function f(x) = 2 + 6x, then what is f(x – 2) simplified as a polynomial?

A: The given function is f(x)=2+6x

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 the rational zeros of the function f(x) = x3 − 7x − 6 .

A: Given the function f(x) = x3 − 7x − 6 . We need to find the rational zeros of the function.

Q: Sketch the graph of the function g(x) = −x2 + 10x − 16 by (a) applying the Leading Coefficient Test,…

A: Given: Sketch the graph of the function g(x) = −x2 + 10x − 16 by (a) applying the Leading…

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A: Give a polynomial function f is divided by x - c

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Q: Find a degree 3 polynomial having zeros -2, 1 and 8 and the coefficient of x3x3 equal 1. The…

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Q: Find the remainder R when f (x) = 6x3 + 3x2 + 2x - 11 is divided by g(x) = x - 1. Is g a factor of…

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Q: Find the leading term of the polynomial function. f(x) = 3x45x² + 3x - 8 0x4 3 8 3x4

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Q: Use an appropriate Chebyshev polynomial to economise f(x) = x³ + 2x² – 5 once

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Q: Find the equation of a 4th degree polynomial that has zeros at x=-7x=−7,  x=2x=2,  x=3x=3  and…

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Q: When a polynomial function f is divided by x-c , the remainder is .....................

A: Remainder theorem states that if a polynomial px is divided by x-a then  the remainder is pa.…

Q: find the degree of the polynomial f(x)=-x2+5x-19

A: Degree of a polynomial is the highest power of variablex of all the terms in the polynomial. For…

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Q: If the zeros of the polynomial f (x) =x3-3x2+x+1 are a-b,a,a+b .find

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Q: Find the zeros of the quadratic polynomial f(x) =6x2 -3,and verify the relationship between the…

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

A:

Q: express f(x) =x³+2x²-x-3 , in term of lagendre polynomial

A: To express the given function f(x)=x3 +2x2 -x-3 in terms of Lagendre polynomial.

Q: Find all the zeros of the polynomial f(x)=2x^3-5x^2-4x+3

A:

Q: Find the x-intercepts of the polynomial function. f(x) = x3 – 3x2 - x + 3 (x, f(x)) : |(smallest…

A: f(x)=x3-3x2-x+3

Q: Find a polynomial of degree four that has zeros -3, 0, 1, and 5, and the coefficient of x3 is -6.

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Q: Find the zeros of the polynomials f (x)=x'-5x² – 2x + 24, If it is given that the product of its two…

A: *to find:- roots of the given equation.

Q: Evalute the polynomial at x= -2    5x^4-3x^2 - x + 1 + 5x^3

A:

Q: If x^3=3x^2, then what is x using the Zero-Product rule?

A: Given that x3 = 3x2.

Q: Find a degree 3 polynomial having zeros -5, 2 and 8 and the coefficient of x3 equal 1

A: By the factor theorem, the required polynomial have factor(x+5),(x-2) and (x-8)   Therefore the…

Q: Find the zeros of the polynomial funtion. x) = x 3+7x2–4x -28

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Q: What is the polynomial function for f(x)= (x^2-3)(2x^2-9)?

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Q: Find all zeros of the polynomial f(x) = 2x^3 + x^2 − 4x + 1.

A:

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

A: Consider the polynomial  fx=x3−5x2−16x +80

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

A:

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: FInd

A:

Q: How should the polynomial function f(x)= }x- +11x + 2x* be written in standard form? A. f(x)= 11x* +…

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A: For evaluating any polynomial f(x) = ax3+bx+c. at x=x0 . replace the value of x with x0 Therefore at…

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: Given the function f(x) = 2 + 6x, then what is f(x – 2) as a simplified polynomial?

A: The given function is: f(x)=2+6x

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A: The given polynomial is y=x-32x+1x-1.

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A: We will solve the problem

Q: When we write the polynomial function that has 0,1,2 as the zeros, the resulting polynomial is -2x +…

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A: A = -3.04 B = 8.04

Q: Find the third degree polynomial function that has zeros -10 and -12i, and a value of 1,776 when x=2

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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