Let an be the leading coefficient. a) Find the complete factored form of a polynomial with real coefficiants f(x) that satisfies the conditions. b) Express f(x) in expanded form. degree 4; an =6; zeros 1, -1, 5i, and -5i a) f(x) = ______ (Simplify the answer. Write the answer in factored form. Use integers or fractions for any numbers in the expression. Express complex numbers in terms of i.) b) f(x) = ______ (Simplify the answer. Use integers or fractions for any numbers in the expression.)

Q: Find a polynomial P(x) with rational coefficients that has the degree 5 and zeros -2,1+2i and -1-2i…

A:

Q: Write a polynomial of degree 3 that has zeros: 3 and 5i. Write the final answer in polynomial form…

A: Given zeros are 3 and 5i complex roots occurs in conjugate pairs ∴ All the zeros are 3, 5i and -5i

Q: Consider the polynomial (x − a)(x − b) and the real number line shown.(a) Identify the points on the…

A: Given:           (x−a)(x−b)

Q: 6. Find all real zeros of the polynomial and write the polynomial in factored fe Rx) = x² – 4x² +x…

A:

Q: Ise the Factor Theorem to find all real zeros for the given polynomial function and one factor.…

A:

Q: Let a, be the leading coefficient. (a) Find the complete factored form of a polynomial with real…

A:

Q: find a polynomial function p(x) having a leading coefficient 1, least possible degree, real…

A:

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: All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in…

A: P(x)=x3+3x2-x-3To find the zeroes of the polynomial, let…

Q: Find a degree 3 polynomial with real coefficients having zeros 5 and 4i and a lead coefficient of 1.…

A: Here I am attaching image so that you understand each and every step.

Q: e the intermediate value theorem to show that the polynomial function has a real zero between the…

A:

Q: Find a polynomial with real coefficients that has the given zeros. -1 and 3-5i One such polynomial…

A:

Q: 13) Use the Factor Theorem A) Is (x-1) a factor of f(x) = 5x* -9x' +19x-27x+12. If it is, then find…

A:

Q: Write the general polynomial p(x) whose only zeros are 1, 4, and-3, with multiplicities 3, 2, and 1,…

A:

Q: Let an be the leading coefficient. (a) Find the complete factored form of a polynomial with real…

A:

Q: Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example…

A: Given: Polynomial of degree 4,           px=x4-7x3+14x2-3x-9 Objective is to find the zeros of…

Q: Find all the real zeros of the polynomial. Use the quadratic formula if necessary, as in Example…

A:

Q: Write the general polynomial q (x) whose only zeros are-3 and 7, with multiplicities 3 and 7,…

A: Explanation of the answer is as follows

Q: Choose all possible zeros of the polynomial of h(x) = 5x³ – 5x² – 10x. %3D | O x = 2 Ox = 0 x =-1 x…

A: Set h(x) = 0. If h is zero of h(x), then h is the factor of constant term.

Q: Write a polynomial in factored form with least possible degree having zeros at -4, -2, 3i, 1-4i, and…

A:

Q: 18. Factor the polynomial into linear factors and sketch the polynomial. P(x) = x* + x3 - x2 +x-2

A:

Q: Find a polynomial p with real coefficients that satisfies the following: The zeros of p are c =+ or…

A:

Q: Use the given zero to find the remaining zeros of the polynomial function. (Enter your answers as a…

A:

Q: Write a polynomial function f of least degree that ha a rational coefficients, a leading coefficient…

A: The given roots of the polynomial: 3, 4+2i, 1+7 Now we have to find the polynomial of least degree…

Q: Let a, be the leading coefficient. Degree 3, a, = - %3; zeros 1 + i and 4. (a) Find the complete…

A: If a+ib is root of the polynomial then a-ib is also root of the polynomial.

Q: a. Apply Horner's rule to evaluate the polynomial p(x) = 3x5 – 2x* + x³ – 2x + 5 at X = -2. b. Use…

A: We will find p(-2) , remainder and quotient as following.

Q: Write a polynomial ƒ(z) of degree 3 given zeros 4and 5i

A: Given a polynomial f(x) of degree 3 and zeros : 4 and 5i We know, complex zeros occurs in conjugate…

Q: DISCOVER: Nested Form of a Polynomial Expand Q to prove that the polynomials P and Q are the same.…

A: Given P(x)=3x4-5x3+x2-3x+5Q(x)=3x-5x+1x-3x+5R(x)=x5-2x4+3x3-2x2+3x+4 Expand Q Q(x)=3x-5x+1x-3x+5…

Q: Suppose that R(x) is a polynomial of degree 9 whose coefficients are real numbers. Also, suppose…

A: Rx is a polynomial of degree 9 whose coefficients are real numbers. Also suppose that Rx has…

Q: Write a polynomial function  f​ of least degree that has rational coefficients, a leading…

A:

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

A: Given equation, x3-43x+42=0        ...(1)

Q: Write a polynomial f(x) that satisfies the given conditions. Express the polynomial with the lowest…

A:

Q: Write a polynomial function f​ of least degree that has rational coefficients, a leading coefficient…

A:

Q: Use the Factor Theorem to determine whether x-c is a factor of f(x). 14) f(x) = x3 + 2x2. 6x + 8;…

A:

Q: Completely factor the polynomial f(x)=x²-24x³ +215x²-852x+1260. Hint f(x) has a double root

A: Let's find factor of given polynomial.

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

A: Explanation of the solution is given below..

Q: Find the remaining zeros of a polynomial with real coefficients and having the specified degree and…

A:

Q: Write a polynomial function f of least degree that has rational coefficients, a leading coefficient…

A:

Q: All the real zeros of the given polynomial are integers. Find the zeros, and write the polynomial in…

A: To find zeroes of polynomialP(x)=x4-2x3-3x2+8x-4

Q: 6) Given the polynomial W (x) = x³ – 2x2 – 3x + 10: a) Find all the zeros, real and complex, of the…

A:

Q: A polynomial P is given. Find all the real zeros of P, and factor P completely into linear and…

A: The zeroes of a polynomial are the values of the variable at which the value of the function is 0.…

Q: Find a degree 3 polynomial with real coefficients having zeros a = 2 and a = 2 - 2i and a lead…

A: If a+ib is a root of a polynomial with real co-efficients then a-ib is also root of that polynomial.

Q: The Missing Coefficient Consider the polynomial function P(x) = x* - 3x + ax² – 6x + 14, where a is…

A:

Q: Find a polynomial f (x) of degree 3 with real coefficients and the following zeros. 2, 3+i s(4) = 0…

A: Given  X =2,3+i

Q: A polynomial expression of degree three is shown below. x²- 3x-4x + 12 Which expression represents…

A:

Q: Write a polynomial function  f​ of least degree that has rational coefficients, a leading…

A: Introduction:  The term "polynomial" refers to a sort of expression. A mathematical statement…

Q: Let a, be the leading coefficient. (a) Find the complete factored form of a polynomial with real…

A: Given conditions: Degree:4 an=45    , zeros: -4i and 5i

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

A:

Q: ONORS ind all exact simplified solutions to this polynomial. 4 - 5x +3 = -4x2-9 Select all that…

A:

Q: 10 Roger factored a polynomial to determine that the zeros of the polynomial are located at x = - 5,…

A:

Polynomials

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