a)list all the possible rational roots using Rational Root Theorem. b)Using synthetic division, express the polynomial equation in factored form. c) List the roots of the polynomial equation.

Q: A fifth degree polynomial with constant coefficients may have (1) 5 distinct real roots. (II) 3…

A: This question can be solved by using the concept of nature of roots of n degree polynomial.

Q: Using the rational root theorem for the polynominl a" – 2r² + 2 – 12,

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Q: If a + bi is a root of a polynomial equation with real coefficients, b + 0, then. equation. is also…

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Q: Use the Rational Zeros Theorem to factor into one linear and one quadratic factor: (2x^3+ 3x -5…

A: Solve the given polynomial by Rational zero theorem.

Q: Given the polynomial y = 2x3 + 28x² + 99x + 7, • list the possible rational roots: • Of these…

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Q: Find the polynomial equation whose zeros are 2 of multiplicity 2, 1 and -2

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Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use…

A: Solution

Q: Use synthetic division to divide, where the result involves a complex number. Specify the quotient…

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Q: Factor the polynomial 4x 4-28x 3+ 61 x2 - 42x+9 and find its zeros given that one of its zeros (of…

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Q: 7.4x+4x3-2Sx2 -x+ 6 0 XI =-3

A: Since you have asked multiple questions, as per company guidelines we will solve the first question…

Q: Use the rational roots theorem to find the possible roots of the following polynomial equation: 10x…

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Q: must every polynomial equation with real coefficients of degree 3 have at least one real root? Why

A: Recall: Fundamental theorem of Algebra: Any polynomial of degree n with real coefficient has n…

Q: | Using the rational root theorem for the polynominl 5z–2²+2-12, what are the values of esting?

A: The given polynomial is p(x)=5x3-2x2+x-12

Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use…

A: Synthetic division: Synthetic division a method of dividing polynomials using the coefficients of…

Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use…

A: Let us use the synthetic division to show that is a solution of the third degree polynomialequation…

Q: What are the rational roots of 15x3 – 32x2 + 3x + 2 = 0 ?

A: To find: The rational roots of the equation 15x3-32x2+3x+2=0. Given: The equation is…

Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use…

A: Given polynomial equation, x3+2x2-2x-4=0

Q: The Fundamental Theorem of Algebra states that any polynomial equation of degree n must have exactly…

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Q: A) find all zeros of the polynomial. Start by listing all possible rational zeros of P and then use…

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Q: The complex zeros of f 1x2 = x4 + 1 For the function f1x2 = x4 + 1:(a) Factor f into the product of…

A: Given :            f(x) = x4 + 1

Q: Suppose that a polynomial equation has the following six roots: -9, -6, 1 + i/2,1 – i/2, 6, and 9.…

A: Here, the required polynomial has six roots: -9,9,-6,6,1+i2, 1-i2

Q: For each polynomial function, (a) list all possible rational zeros, (b) use a graph to eliminate…

A: Since you have posted multiple subparts we solve first three subparts for you to get the solution of…

Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use…

A: Please refer the attached image for complete solution.

Q: Use the remainder theorem to determine if X=-7 is a solution of the polynomial F(x)=3x^2 + 2x^2 -…

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Q: Consider the polynomial equation Question 5 232 +2 0 (a) Using the Rational Root Theorem, show work…

A: (a)Consider the given polynomial:2x3-x2-4x+2=0According to the Rational Root Theorem: If a…

Q: Consider the polynomial equation Question 3: 2x3 4x + 2 0 (a) Using the Rational Root Theorem, show…

A: The given polynomial is say f(x).

Q: A Find the complete set of possible rational roots of the following polynomial equations. 154 2.…

A: To complete the set of possible rational roots.

Q: Prove that a fourth degree polynomial with one real root and real coefficients must have another…

A: Given: Fourth degree polynomial having one real root and if has real coefficient. To Prove: Has…

Q: What steps would you take to find the rational zeros of a polynomial P?

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Q: Find a polynomial with real coefficients, degree 3, and zeros 3 − 2? and −2. Give both the factored…

A: Given, degree=3 zeros are 3,-2, and -2.

Q: Find all possible rational zeros of 3x + 9x + 8x° – 2x2 – 3x – 2. Write all answers as reduced…

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Q: List all possible values that could be roots of the polynomial 4x*- 23x -41x² +59x-18 according to…

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Q: 1. Determine the real zero, and a complex conjugate pair of zeros for the equation below. 5x* – 16x³…

A: Given:      5x4 -16 x3 + 57 x2 + 120 x + 120

Q: ind all the REAL roots of 2x5 + 3x4 – 30x3 – 57x2 – 2x + 24 using Rational Root Theorem with explan

A: Given: 2x5 + 3x4 – 30x3 – 57x2 – 2x + 24

Q: Prove that a fourth degree polynomial with one real root and real coefficients must have another…

A: Since the polynomial is of 4th degree. So, it must have 4 roots . As one of the root is real . So, 3…

Q: What are all the possible rational roots of the polynomial )= -3r+x-37 1.3 B 1.-1.3.-3 1.-1.2.-2. 3.…

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Q: Given the polynomial y = x3 4x2 20x + 3, • list the possible rational roots: • Of these possible…

A: y=x3-4x2-20x+3 Here the leading coefficient is 1 and the constant term is 3. Now the factors of…

Q: Find all the rational, irrational, complex zeros x^4+3x^3-3x^2-15x-10

A: Given information: x4+3x3-3x2-15x-10

Q: Create a polynomial equation with real coefficients that has 2 and 1-i as roots.

A: To create a polynomial equation with real coefficients that has 2 and 1-i as roots.

Q: Given the equation x4 - 6x3 - 5x2 + 24x +4 =0, complete the following. a. List all possible rational…

A: We need to solve for roots.

Q: 1) Divide the polynomial x^3-1 by x-1, and use the result to factor the polynomial completely 2)…

A: Divide the given polynomials and use the result to factor the polynomial completely

Q: What are all the possible rational roots of 2x^3 + 3x^2 - 10x + 4 = 0?

A: Given: - The equation is, 2x3+3x2-10x+4=0 To find: - The rational roots of the given equation.

Q: If a + bi is a root of a polynomial equation with real coefficients, b ≠ 0, then________ is also a…

A: Given: if a+bi is the root of a polynomial equation with real coefficients,b≠0, then ..............…

Q: Find all rational zeros of the equation. 1-4x-1-5x-2+20x-3+4x-4-16x-5 =0

A: Given equation 1-4x-1-5x-2+20x-3+4x-4-16x-5=0. The objective is to find all rational zeros of the…

Q: 6. in

A: We solve the problem by just calculating the equation that given.

Q: What are the possible rational roots of the polynomial equation? Drag the values into the box to…

A: Consider the equation 3x8+11x5+4x+6=0 We have to find the possible rational root. For finding…

Q: In Exercise 1 - 3 a. List all possible rational zeros. b. Use synthetic division to test the…

A: The given function is f(x)=x3-5x2+17x-13=0 .....................(1)

Q: Discuss the possibilities for the roots to : 2x'-5x - 6x+4 = 0 12. 3x - 5x -x² -8x+4 =0

A: We can use Descartes rule of signs to check the nature of possible roots of the given function, P(x)…

Q: use descarts' rule of sign to detemine how many positive, how many negative real zeros and how many…

A: Given polynomial

Q: 17. How can you quickly determine the number of roots a polynomial will have by looking at the…

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Polynomials

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