Consider the polynomial function p(x)=3x^4−x^3−x^2−3x+3. Use polynomial long division to perform the indicated division and rewrite the polynomial in the form p(x)=d(x)q(x)+r(x), where d is the divisor, q is the quotient, and r is the remainder. (3x^4−x^3−x^2−3x+3)÷(x^2−4x+2)

Q: Use synthetic division to perform the division.   x^3+5x^2+8x+6 over x+3

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Q: Determine an equation in fortored form for a polynomial function with zeros x=-3 (order 2) and x = 2…

A: We have to determine an equation in factored form for a polynomial function with zeros: x=-3 order 2…

Q: sketch the polynomial function by finding all critical values. f(x)=x4-x3-20x2

A: Consider the function: fx=x4-x3-20x2 Differentiate the given function with respect to “x” then,…

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

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Q: A polynomial function with leading term 2x to the power of 3 has a degree

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Q: Determine the polynomial function of third degree whose zeroes are  3,7,7

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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: Find a fourth degree polynomial with real coefficients that has zeros of -3, 2, i that passes…

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Q: Find a polynomial that interpolates (-1,4) and (3,6), then find the value of f(x) at x=0 and x= 2.

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Q: Find a polynomial with -3, 0, 4 as zeros, and of degree 3.

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Q: When a polynomial function f is divided by x - c, theremainder is_______

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

Q: Use polynomial long division to divide f(x) = x3 – 5x² + 8x – 2 by x² – 2 and cotient and remainder.

A: To divide the function f(x)=x3-5x2+8x-2 by x2-2  using polynomial long division and to identify the…

Q: express 5x2 - 3x + 6 in terms of Legendre's polynomial.

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Q: How do I find a polynomial function with given zeros and multiplicities?

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Q: Simplify and write the resulting polynomial in standard form and indicate its degree. (5x2 - 7x - 8)…

A: The given expression is (5x2 - 7x - 8) + (2x2 - 3x + 7) - (x2 - 4x - 3).

Q: A simplified polynomial that has three terms is called a/an

A: A simplified polynomial that has three terms is called a/an________

Q: find a polynomial of degree 4 with zeros -6,-1,0, and 3.

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Q: Simplify and write the resulting polynomial in standard form and indicate its degree. (17x3 - 5x2 +…

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Q: A rectangular field is twice as long as its width. If 3 feet are taken from the width, and 4 feet…

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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: Differentiate the function f (x) = (3x2 + x - 2)2 in two ways. (a) Use the general power rule. (b)…

A: To differentiatef(x)=(3x2+x-2)2 in two ways

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: Use synthetic division to divide fx) = x – 4x² + x + 6 by x + 1. Use the result to find all zeros of…

A: given,        fx=x3-4x2+x+6       ,   x=-1

Q: Write a polynomial function with minimum degree andleading coefficient 1 that has zeros x =…

A: If  zero is a and its multiplicity is m, we can write it as (x-a)m

Q: Sketch the graph of the function f(x) = −5x2 − x3 by (a) applying the Leading Coefficient Test, (b)…

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Q: Find a polynomial function of degree three with numbers 3, 5, -2 as zeros of the polynomial.

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

A: Given, If a third degree polynomial has alone x-intercept at x = a.

Q: express the volume of the box as a polynomial function in terms of X

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Q: A rectangle has a length of 18 units and a width of 14 units. Squares of x by x units are cut out of…

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Q: (6x* + 10z³ + 5x² + x + 1) ÷ (x + ,) 31

A: Use Synthetic division to find quotient

Q: Find a polynomial of the specified degree that has the given zeros. Degree 5; zeros -2, -1, 0, 1, 2

A: If a polynomial P(x) whose degree n having zeros x1, x2, ..., xn then the polynomial is…

Q: A simplified polynomial that has three terms is called a/an___________.

A: A simplified polynomial that has three terms is called a/an................

Q: Use synthetic division and the Remainder Theorem to find the indicated function value. f(x) = 5x* -…

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Q: A simplified polynomial that has two terms is called a/an__________.

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Q: Use synthetic division to divide f(x) = x3 - 4x2 + x + 6 by x + 1. Use the result to find all zeros…

A: Given equation is f(x)=x3-4x2+x+6 and the division by x+1. Find all zeros of f.

Q: Simplify and write the resulting polynomial in standard form and indicate its degree. (8x2 + 7x - 5)…

A: Simplify and write the resulting polynomial in standard form and indicate its degree. (8x2 + 7x - 5)…

Q: write a polynomial function of minimum degree in standard form with real coefficients whose zeros…

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Q: Find a third degree polynomial function with zeros 3,-4, and -/-

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Q: find a degree 3 polynomial with zeros -2,1, and 5 and going through the point (0,-3)

A: Assume a polynomial and use the given point.

Q: Find a polynomial of degree 3 that has zeros 5, -5, and 8

A: Given :To determine the polynomial ofdegree 3 has zeros 5,-5 and 8.

Q: Find the polynomial function with real coefficients 3, -1 with multiplicity of 2 and -i. Rewrite in…

A: If x=3 is a zero then (x-3) is a factor. If x=-1 is a zero then (x+1) is a factor. It has…

Q: Find the general polynomial function of lowest possible degree with real number coefficients that…

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Q: - -2x4 + x - 2x² + 3x – 1.

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Q: A simplified polynomial that has two terms is called a/an

A: A simplified polynomial that has two terms is called a binomial.

Q: Find a polynomial of the specified degree that has the given zeros. 0, -1, 5

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Q: Use synthetic division to solve (x' +5x² +5x-2)÷(x+2). x' - 3x – 1 — Зх x – 3x +1 O x +3x-1 х* +3x—1…

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Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

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Q: Express the polynomial x3 + 2x+3 EZ[x]as a product of irreducible polynomials of 75[x]- Attach File…

A: Use the definition of irreducible polynomial and property of ring Z_5[x].

Q: What is a cubic polynomial function in standard form with zeros -4, -5, and 4?

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