Use the Rational Zeros Theorem to factor into one linear and one quadratic factor: (2x^3+ 3x -5 )Hint: do NOT attempt to factor, but instead use the Rational Zeros Theorem. Please step by step

Q: 8x5-3÷X-)

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Q: 2. Calculate (4x³ – 6x² – 14) (x + 6) using long division. Show your work! -

A: Perform long division method

Q: Classify the quadratic forms as positive definite, positive semidefinite, negative definite,…

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Q: Use polynomial long division to divide 4x2 + 23x – 16 by x + 5. What is the quotient and remainder?

A: In long divide method , You need to eliminate the highest term available by dividing.

Q: Give an example and explain why a polynomial can have fewer x-intercepts than its number of roots

A: We need to give an example and explain why a polynomial can have fewer x-intercepts than its number…

Q: This equation is about factoring polynomials. In which factor y^3+512 completely and show work

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Q: Use synthetic division to find the quotient and remainder when: x5 - 4x3 + x is divided by x + 3

A: To find the quotient and remainder

Q: find the equation of a polynomial with the following zeros: 2, -1, 0, 4+i square root 5, 4-i square…

A: In the question we have to find the equation of polynomial  with the following zeros: 2, -1, 0, 4+i…

Q: Write the rule of the quartic (degree 4) polynomial with roots -4, -1, 2, and 3, and у-intercept 30.

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Q: A + 5x3 - x2 - 50x – 90 = 0 if 2 - 10 is one of the factors. Be sure to discuss real and complex…

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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: If a sixth-degree polynomial is divided by a third-degree polynomial, what is the degree of the…

A: We have to find the degree of the quotient polynomial If a sixth degree polynomial is divide by a…

Q: 8x +6x2 -9 3 2х-2

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Q: Do all polynomial equations have at least one imaginary root?

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Q: quotient

A: Solution : The polynomial division for the following quotient of x+5 and the remainder of -2 will be…

Q: Classify the quadratic forms as positive definite, positive semidefinite, negative definite,…

A: A quadratic form in n variable is any function

Q: Use long division to find quotient  x3 + 2x + 4        x - 3

A: By using long division find quotientx3+2x+4x-3

Q: Find the quotient of the polynomials using SYNTHETIC DIVISION. Show your solution. (2x + x3 + 7x2 -…

A: We need to find the quotient of the polynomials using SYNTHETIC DIVISION (2x + x3 + 7x2 - 40) ÷ ( x…

Q: 8. Factor the polynomial r– 2x2 - x-28 into linear factors. Begin by using a graph to | find a real…

A: Given that polynomial fx=x3-2x2-x-28Solution put x=3fx=x3-2x2-x-28f3=33-232-3-28=-22f3≠0x-3 is not a…

Q: One example of an equation (cubic using the remainder or factor theorem)

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Q: Use polynomial long division to find the quotient and the remainder when 2x – 2x2 – 3x + 1 is…

A: Polynomial long division: - A long division polynomial is a form for dividing a polynomial by a…

Q: Express the area of the polygon as a polynomial. 41. Rectangle 42. Right triangle 6x - 1 4x² - 1…

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Q: Enter a quadratic polynomial which has roots at 2/17 and -9.

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Q: Express as a polynomial.

A: We know the identity that, a-ba+b=a2-b2                  ⋯⋯1a-b2=a2+b2-2ab       ⋯⋯2 We have the…

Q: Explain how to find the degree of a polynomial in two variables.

A: We have to explain how to find the degree of a polynomial in two variables.

Q: Determine the equation of a quadratic function given zeros x=4 and point (3, 2)

A: Equation of quadratic function is given by as y = a(x-p)(x-q) Where x,y = passing point p,q = roots…

Q: How to determine the quadratic and repeated factors within the denominator?

A: Given: Used Formula: Find: The quadratic and repeated factors in the denominator.

Q: Use long division to find the quotient and the remainder when the function f(x)= 6x³ – 35x² – 98x –…

A: We will use long division first To factorize the polynomial, we will find the roots of equation

Q: Make up a polynomial that factors into a perfect square.

A: Let the polynomial be: x2-6x+9 We express it in the form of a perfect square as follows:…

Q: Use synthetic division to find the quotient and remainder when                   x3 - 4x2 - 5 is…

A: We have,  Dividend=x3-4x2-5Divisor=x-3 Therefore, x3-4x2-5x-3 Take the constant term of the divisor…

Q: Factor completely x5 - x, or state that the polynomial is prime.

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Q: Find the quadratic polynomial whose zeroes are -3 and 4

A: Solution:- We know that a quadratic polynomial can be written in the form of P(x) =x2 - (α + β)x +…

Q: One of the zeroes of the polynomial 2x2+7x-4 is

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Q: Solve using polynomial long division and give the quotient and remainder.  x^4+6x^3-2x+4 / x+1

A: Topic = Algebra

Q: What are the real or imaginary solutions of the polynomial equation?

A: If the solutions of the polynomial is from the real number set, then then the solution of the…

Q: Use Synthetic Division to find the quotient and remainder when the first polynomial is divided by…

A: Given,

Q: Divide the first polynomial by the second polynomial using the long division method.  Show complete…

A: We need to divide x3+3x-4x2-12   by  x-4 x3+3x-4x2-12  can also be written as x3-4x2+3x-12  Hence,…

Q: Use the quotient rule to divide and simplify. square root of 162x^2 / x^4

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Q: What are three real-world polynomial applications and how do they impact society?

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Q: Find a polynomial equation that passes through the points (1,3), (0,1), (1,3)

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Q: Express as a polynomial. (3x - 4)(2x + 9)

A: 3x-42x+9

Q: Use synthetic division to find the quotient and remainder when: 3x3 + 2x2 - x + 3 is divided by x -…

A: Given: The expression 3x3+2x2-x+3÷x-3, To find: The quotient and remainder of the given expression…

Q: Find the quotient and the remainder when x4 - 3x3 + 2x - 5 is divided by x2 - x + 1

A: To divide x4-3x3+2x-5 by x2-x+1, use the long division method.…

Q: If a fifth degree polynomial is divided by a third degree polynomial, what is the degree of the…

A: Let there be two polynomials fx=ax5+bx4+cx3+dx2+ex+f and gx=mx3+nx2+px+q where a≠0, m≠0.

Q: Use synthetic division to find the quotient and remainder when x4 -4x2 + 2x + 5 is divided by x -2.

A: Given polynomial expression:                                                x4-4x2 +2x +5 and test…

Q: Determine a positive real root of this equation using appropriate software: 2x3 − 10x0.5 − 3x = −3

A: Consider the given equation as 2x3-10x0.5-3x=-3

Q: Express as a polynomial. (2x + 5)(3x _ 7)

A: Given: 2x+53x-7

Q: Classify the quadratic forms as positive definite, positive semidefinite, negative definite,…

A: Consider the following quadratic form: x12+2x22 Compare above quadratic form with…

Q: Create an equation for a polynomial whose roots are x = -1, -5, 3 with a y intercept of 8.

A: Given :   Roots : x= -1, -5, 3