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

Q: 47. For what value of k will the polynomial function f(x)=x²+6x² +kx -4 have the same remainder when…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: 10. Write a third-degree polynomial f(x) with integer coefficients and zeros of 5, -, and 4.

A: Let the polynomial is  fx=αx-15x--23x-4=αx-15x+23x-4=α5x-153x+22x-4 Coefficient will be integer if α…

Q: How many inflection points can a: (a) quadratic polynomial have? (b) cubic polynomial have? (c)…

A: fx be a qudratic polynomial .⇒f''x=constant xtherefore a quadratic polynomial never has any…

Q: 1. When the polynomial 6x -ar' + bx² +3x+4 is divided by x+1 the remainder is 10. When it's divided…

A:

Q: Find the polynomial of the lowest possible degree which assumes the values 3, 12, 15, 21 when x has.…

A:

Q: What are the zeros of the polynomial p (x) = (a - 5) (3x + 5) (x2 – 7x + 12)? %3D Express them in…

A:

Q: polynömial that passes through the three points (0, 1), (1, 2) and (2, 23). If the coefficient of x…

A:

Q: 4. If x=-4 and x=1 are the roots of x* + 3x' - 3x +3x – 4 = 0, find the other two roots of the…

A:

Q: Express as a polynomial. (t 2 + 2t - 5)(3t 2 - t + 2)

A: Given: t2+2t-53t2-t+2 For the polynomial, we solve the parenthesis,…

Q: A certain polynomial has a root with a multiplicity of 3. What does this tell you about the behavior…

A: Given: A certain polynomial has a root with a multiplicity of 3.

Q: 19) Determine a polynomial that represents the area of a square having sides of length s x + 8. B)…

A:

Q: How many roots are there for the polynomial that factors into f(x) = (x² – 1)(x + 2)(æ – 1)2? 3.

A: no of roots = ?

Q: 14. Form a quadratic polynomial whose one zero is 8and product of the zeros is -56 15. If the zeros…

A: We have to find out quadratic polynomial

Q: Test the polynomial x – 2x3 + 6x – 3 for irreducibility over Q.

A: We have to check whether the polynomial x4-2x3+6x-3 is irreducible over the set of rational numbers…

Q: 9. When the polynomial mx' – 3x² + nx +4 is divided by x - 3, the remainder is 16. When it is…

A:

Q: 5. For how many different integers bis the polynomial x² + bx + 16 factorable over the integers?

A: From the given data

Q: What is the largest multiplicity in the factored polynomial y = (x2 – 1)(x + 2)(x + 4)?

A: Here function is :  y = (x2 - 1) (x +2 ) (x+4)  It can be written as  y = ( x - 1)( x + 1 )( x + 2)(…

Q: Now let's attempt to work a similar problem backwards. Suppose you have a polynomial with leading…

A: Given  Leading coefficient =12 constant=15

Q: 7. What is the constant term of the polynomial expression: x* – 2x + x² – 5x + 6? А. 1 8. Express:…

A: Let's find.

Q: find the polynomial of degree 3 with zeros that include 3i, 3 and P(1)=3

A: The given zeros of a polynomial function are 3i and 3.

Q: 1. Factor completely. a. 64t² – 49r2 b. т? — 6т —16 с. x² + x – 20 - - -

A: Factorization:- Factorization or factoring consists of writing a number or another mathematical…

Q: Select the factors that multiply to create a polynomial with this description: (1) As x→-0, y→-∞ (2)…

A: Given x→-∞ and y→-∞ and x→∞ and y→∞ and x=4 is a root

Q: 18. Express the polynomial 6x -x +2x-4 in standard form. 6x'-2x-4 7 +2x-4 -4+2x-5x 5x +2x-4

A: standard form is the form in which polynomial is written decreasing power of x and all different…

Q: Give the degree of the polynomial. 7 9 -vy

A:

Q: 5) If the leading term of a polynomial is -2x18, what do you know about the end behavior? As x → 0…

A: We will find the end behavior of the polynomial when Leading term is given.

Q: Suppose 34 is a root of a polynomial equation. What does this tell us about the leading coefficient…

A: we have been given that the root of a polynomial equation is 34. we have to tell about the leading…

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

A:

Q: 13. What are the roots of the polynomial equation: x3 + 6x2 + 3x – 10 = 0? A. 1, 2 and 5 B. 1, -2…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q3) Write in factor form a 5h degree polynomial whose zeros are +2, -2 and 4 with multiplicity 3

A:

Q: 1. It is known that the polynomial p(x) = 2 – (x + 1) + x(x + 1) – 2æ(x + 1)(x – 1) interpolates the…

A: Solution by using Newton's forward difference interpolation method .

Q: For what value of a will five of the six real roots of 6x6 + 7x5 _ 43z4 - 153 + 49z2 + ax polynomial…

A: For what value of a will five of the six roots of polynomial P(x) be shared by the polynomial Q(x)

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

A:

Q: * The Simpson's Rule gives the exact result when applied to any polynomial .of degree-➖➖➖➖➖➖➖or less…

A: Simpson's Rule: It is a numerical method for approximating the integral of a function between two…

Q: 4. When the polynomial P(x) is divided by (x-2)2 the remainder is 3x - 3. What is the remainder when…

A:

Q: What is the leading coefficient of a third degree polynomial function that has an output of 1272…

A: Given zeros of the third-degree polynomial, -6, 7i, and -7i

Q: 12. The second-degree Maclaurin polynomial for f(x)=vx+9 is 3+ x² If this 6 108 polynomial is used…

A: The Maclaurin polynomial for f(x)=x+9is 3+x6-x2108 To approximate 8, substitute -1 for x in the…

Q: 21) Determine a polynomial that represents the area of the figure. 21) 2x + 6 3x + 3 A) 6x2 + 18 B)…

A:

Q: The polynomial p(x) has the rest (x+2) when dividing it by (x^2+2x-3) and the rest 1 when dividing…

A: We have given that  p(x) leaves the remainder (x+2) when divided by x2+2x-3 and  p(x) leaves the…

Q: what could be a polynomial with a degree of 5 if its zeros are -2,1, and 4?

A: The given zeros are, –2, 1 and 4.

Q: 42. What is the polynomial equation whose roots are {-2, 2, and 4 of multiplicity 2} A. 2x* - 2x +…

A: As per bartleby guidelines we only give first question answers.

Q: 2) When a polynomial, ax-3x² - bx - 5 is divided by the binomial (x-3), the remainder is 10. When…

A:

Q: #7: For what value of k will the polynomial function f(x)=x'+6x² +kx=4 have the same remainder when…

A: The Polynomial Remainder theorem states that if x-b divides the polynomial, Qx, then the remainder…

Q: 7. Find all the zeros of the polynomial: y = 2x* – 5x³ + 10x – 12. - -

A:

Q: 8) If x = 2 is a zero, what are the other zeros for x3 – x2 - x- 2 = 0 ?

A:

Q: If x = -1 is a root of the polynomial 0 = æ³ + 2x2 – 5z – 6. what are the other roots? Ox =-3, x = 2…

A: see next step

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: A polynomial f(x) = x³ + ax² – 3x + b when divided by 91 (x) = x – 2 gives a remainder of 6 and f(x)…

A: Given:             fx=x3+ax2-3x+b using remainder theorem: fx=x3+ax2-3x+b is divisible by g1x=x-2…

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

A:

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

A: Given:The sum of two polynomials each of degree 5 will be less thanor equal to degree 5

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.