Explain why all Odd degree Polynomials with Real Coefficients have a Real Root.

Q: Why is a polynomial be thought as adding terms, even if some coefficients are negative

A: Why is a polynomial be thought as adding terms, even if some coefficients are negative

Q: If a polynomial equation is of degree n, then counting multiple roots separately, the equation has…

A: If a polynomial equation is of degree n, then counting multipleroots separately, the equation has…

Q: Can someone answer all of these polynomials?

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Q: A simplified polynomial that has exactly one term is called a/an__________ .

A: A polynomial that has exactly only one non-zero term is called a monomial. Also, each term of the…

Q: what are terms of polynomials?

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Q: The polynomial x(x^2-4)(x^2+4) has___ real roots.

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Q: Suppose is a root of a polynomial equation. What does this tell us about the leading coefficient and…

A: Consider an example of a quadratic equation. The quadratic equation with the roots α and βis written…

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

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Q: A simplified polynomial that has exactly one term is called a/an ............ ?

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Q: Form a polynomial with zeros: -6, multiplicity 1; 2 multiplicity 2; degree 3

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Q: Explain why the degree of the product of two nonzero polynomials equals the sum of their degrees.

A: Let the two polynomials be of degree m & n respectively. Then, the highest power of x in the…

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

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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: 3. x – 6x² + x

A: We know that a polynomial with its highest degree 3 is known to be a Cubic polynomial. The general…

Q: The number of polynomials having zeroes as -2 and 5 is

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Q: What is a polynomial in x?

A: The x happening in a polynomial is generally referred to as a variable or an indeterminate. When the…

Q: Explain the formula for the Hermite interpolating polynomial?

A: In any polynomial function if the values for the function is known for some data points and the…

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

A: Explained below

Q: Explain Newton Raphson method of finding root of the polynomial.  (will leave a like)

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Q: - Use Descartes' rule of signs to get an upper bound on the number of real roots of the polynomial…

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Q: 3. What is the number of coefficients of a polynomial of degree n in two variables? In three…

A: Given: A polynomial of degree n.

Q: A simplified polynomial that has exactly one term is called a/an

A: Given: A simplified polynomial that has exactly one term is called a/an ......... Concept Used: A…

Q: Write the resulting polynomial in standard form and indicate its degree. (13x4 - 8x3 + 2x2) - (5x4 -…

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Q: How do you write polynomial funtions in standard form when the zeros are 5, 3i, and -3?

A: The polynomial with zeroes as a, b and c can be expressed as (x - a)(x - b)(x - c). This can be…

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

A: In f(x)= x4+x3+7x2+9x-18 there is only one change of sign. So, this polynomial can have 1 positive…

Q: determine if the statement is true or false. If a statement is false, explain whyThe product of two…

A: Statement: The product of two polynomials each of degree 4 will be less than degree 8.

Q: 12. Explain how to find the degree of a polynomial

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Q: What is the polynomial of degree zero

A: Degree of Polynomial: In a polynomial highest power of variable is called degree of polynomial.

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

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Q: Describe the number and type of roots for the polynomial (number of real and complex).  x3 + 2x2 –…

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Q: What does the Fundamental Theorem of Algebra tell us about a polynomial over real numbers?

A: Use the definition of theorem

Q: Discuss the properties of polynomials

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Q: Find a polynomial degree 3 with constant term 96 and zeros 3 and 4 (multiplicity by 2)

A: Let Px be a polynomial of degree 3 with constant term 96 and zeros 3 and 4 (multiplicity  2). A…

Q: Explain why the degree of the sum of two polynomials of different degrees equals the larger of their…

A: If two polynomials are given then their sum is calculated by adding the coefficients of the…

Q: Find a polynomial (fx) of degree 3 that has the following zeros. -4, (multiplicity 2), 3 Leave…

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Q: Exercises: 1. Using the fact that 3x² +7x – 9 = ((((3)x) + 7)x) – 9), show how to produce this…

A: To find: number of smallest steps used in producing x8 +x4

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: What are polynomials and can you give me an example of a few?

A: Concept of polynomial is used .

Q: Suppose you are asked to construct a polynomial with -3, 1, and 5 as roots. There are an infinite…

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Q: We can apply Eisenstein criterion for irreducibility of the polynomial 4x10−9x3+24x−18 over Q. true…

A: Using Eisenstein Criterion for irreducibility of f(x) over Q,

Q: When are the non-negative integer and the real constants called the coefficients of the polynomials?

A: When the non- negative integer and the real constants are expressed as linear combination of finite…

Q: What is a polynomial?

A: A polynomial is an expression consisting of variables and coefficients, involving the operations of…

Q: Write a polynomial o fminimum degree in standard form with real coefficient whose zeros include 4,…

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Q: To find the possible roots of the polynomial 4x3 + x4 - 7x² - 8x - 8

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Q: What is understood by the term degreeof a polynomial?

A: Degree of a polynomial: