In a polynomial function, if the third differences are not constant, but the fourth differences are, then the function is: a) Constant b) Linear c) Quadratic d) Cubic e) Quartic

Q: . Do the polynomials x? + 2, 2x? – x + 1,x + 2, and x² + x + 4 span P2?

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Q: The remainder theorem indicates that if a polynomial flx) is divided by x - c, then the remainder is

A: We have to fill in the blanks: The remainder theorem indicates that if a polynomial fx is divided by…

Q: x4 + 9x3 + 22x2 + 19x + 45; c = -3

A: According to remainder theorem, if we plug the given number -3 for x, and -f -3 is a zero, then the…

Q: Find all zeros of the polynomial function. Ax) = x* - 2x + 8x2- 32x – 128 O -4, -4, -2, and 4 O -4,…

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Q: Given that π is not the zero of a nonzero polynomial with rationalcoefficients, prove that π 2…

A: Let us consider a function  f(x)= x2 - ax - b Where a and b are rational  So, f(x) a polynomial with…

Q: use the remainder theorem to determine if the given number, c, is a zero of the function. A, f(x) =…

A: Given: f(x)=2x4-3x2+5x-11;c=2 f(x)=2x3+5x2+14x-35;c=7 f(x)=x3-7x2+16x-10;c=3+i (a) If c=2 is a…

Q: If alpha and beta are zeroes of x^-x-30,then form a quadratic polynomial whose zeroes are –2alpha…

A: α & β are zeroes of x2-x-30. That is, α+β=--11  &  αβ=-301   ∵If α & β are zeroes of…

Q: Let a be a positive real root of the polynomial 2x + 10x4 + 20x3 – 10 (you can use a graphing tool…

A: We have to prove that α is not a constructible number.

Q: xpress the polynomial in factored form p(x)=x^3-x^2-8x+12

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Q: Do the polynomials x? + 2,2x2 – x + 1,x + 2, and x² + x + 4 span P2?

A: Let u1 = x2+2, u2 = 2x2-x+1, u3 = x+2, and u4 = x2+x+4. Notice that u1 + u3 = u4. So, u1, u2, u3,…

Q: Create a polynomial tl

A: Given,  Zero of c=1, Multiplicity =2, Degree=3, a=2 To create the polynomial

Q: Use the Remainder Theorem to show that X+1 is a factor of 19x42 + 18x -1.

A: we have to divide the equation 19x42 + 18x -1 by x+1 by remainder theorem so, for that we will first…

Q: Find all real zeros of the polynomial function, n

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Q: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Given polynomial                    P(x)=8x3+10x2-39x+9

Q: In the given question , determine whether the statement is true or false. If it is false, explain…

A: fx=4x+32x-1 calculate the values of f(x) for given values of x x 100 101 102 103 104 105 106…

Q: Write an eighth-degree polynomial in factored form that is decreasing at both ends, has a single…

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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: The Remainder Theorem states that if the polynomial f(x) is divided by x - c, then the remainder is…

A: Given Data :  The polynomial fxis divided by x-c        To Find : Remainder The polynomial  fx is…

Q: According to Descartes' Rule of Signs, how many positive zeroS could the polynomial x* + 5x* – 2x² –…

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Q: The graph of a quartic polynomial f(x) with integer zeros is shown to the right. Write the complete…

A: We have to find the expression.

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: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Perform synthetic division on the polynomial. -If the entries in last row alternate in sign then a…

Q: Write a polynomial with zeros 0,-3, and 2 with multiplicities 2. 1, and 2, respective What is its…

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Q: The Linear Factorization Theorem states that an nth-degree polynomial can be expressed as the…

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Q: The ________ Theorem states that if a polynomial f(x) is divided by x − k, then the remainder is r =…

A: The ________ Theorem states that if a polynomial f(x) is divided by x − k, then the remainder is r =…

Q: What is the polynomial, in factored form, for the function with the leading coefficient 6, and zeros…

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Q: 1. Determine whether the set S = {2x² – 14x + 34, 3x – 4, x² + 5x + 1} is linearly independent or…

A: Here first we check the set s is linearly dependent or not.

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: The Linear Factorization Theorem states that an nth-degree polynomial can be expressed as the…

A: The Linear Factorization Theorem tells us that a polynomial function will have the same number of…

Q: If a polynomial f(x) has a remainder of -9 when divided by a 3, what is f(3)?

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Q: Find a polynomial with integer coefficients that has 1/2 and -1/3 aszeros.

A: Since the required polynomial is to have two zeroes, it's degree should be 2 i.e. It should be a…

Q: Find a quadratic polynomial such that f(1) = 5, f'(1) = 4, and f"(1) = 8.

A: The quadratic polynomial is of the form: f(x)=ax2+bx+c...(1) Now,…

Q: 13) Use Descartes' Rule of Signs to determine how many positive and how many negative zeros each…

A: We have to use Descartes Rule Of signs to determine positive  and negative roots   Given function…

Q: Find a, beR such that the polynomial f(x) = 6x4 – 7x3 + ax? + 3x + 2 is divisible by g(x) = x2 – x +…

A: When a polynomial is divisible by another polynomial, there is a quotient polynomial. The leading…

Q: What is the fermat value, in polynomial form, of integer 'a', if a=x^4 + 1; p=x^2 + 1?

A: We have to find the Fermat value 'a' which is given in the following form, a=x4+1p=x2+1

Q: Use the Factor Theorem to find all real zeros for the given polynomial function and one factor 2x3 +…

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Q: Use the remainder theorem to evaluate the polynomial for the given values of x. h (x)=9x'-x-45x+5

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Q: Enter a quadratic polynomial which has roots at 13/6 and -4

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Q: By applying divisionalgorithm prove that the polynomial g(x) = x² +3x +1 is a factor of the…

A: Here we have to apply a division algorithm to prove that the polynomial g(x)=x2+3x+1 is a factor of…

Q: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Here we have ;  P(x)=3x4-5x3-2x2+x-1

Q: Use Descrates's Rule of Signs to determine how many positive and how many negative real zeros the…

A: Using Descartes' rule of signs, determine the possible number of positive and negative real zerosof…

Q: Show the quadratic formula work that reveals the two non-real zeros of the polynomial function…

A: We don't have any general formula for finding zeros of polynomials having degree more than 2, hence…

Q: A ____ is a polynomial that has two terms, and a _____is a polynomial with three terms.

A: We have to fill in the blanks: A ____ is a polynomial that has two terms, and a ____ is a polynomial…

Q: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

A: Given: Show that the given values for a and b are lower and upper bounds for the real zeros of the…

Q: The Remainder Theorem states that if the polynomial f(x) is divided by x - c, then the remainder…

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Q: Show that a cubic polynomial x3 + Ax2 + Bx + C has one real zero and two pure imaginary zeros only…

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Q: Construct a polynomial with Z coefficents with a root of the given C 2+ V7 (d) 3 (e) V3+ v2

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Q: suppose a polynomial function of degree 3 has zeros -1/3,2, and 8. factor the function over the real…

A: To determine the factors of the polynomial.

Q: Determine if the statement is true or false. If a statement is false, explain why?The sum of two…

A: To find:  If the statement, the sum of two polynomials each of degree 5 will be degree 5, is true or…

Q: Consider a quadratic polynomial with a negativ main coefficient and a negative discriminant. Which…

A: Consider a quadratic polynomial with a negative main coefficient and a negative discriminant. Which…

Polynomials

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