14. fx)= (4x - 11x+2)(7x - 2x)+(4x +9 x)(4x -9x+1) (b) 13 (c) 14 (d) 15 (e) 16 (a) 7 (b) 8 (c) 9 (d) 10 (e) 11 15. Determine which of the following polynomials has at least one real zero

Q: 2. Use syntr dhe hirst polynomial by the second. а. х2+x -3; х-1 b. 4x- 3x2+ 3x - 2; x-1 c. x'+x°…

A:

Q: Make up two polynomials, not of the same degree, with thefollowing characteristics: crosses the…

A: Here it is given that Polynomial  crosses the x-axis at - 2  touchesthe x-axis at 1, and is above…

Q: 1. Show whether the given polynomials 1+4x + x², 2+ 5x + 3x2, 3x 5x, and 3+ 15x - 8x spans p,.…

A:

Q: Determine whether the first polynomial can be expressed as a linear combination of other two…

A: The given polynomials are  2x^3 − 2x^2 + 12x − 6, x^3 − 2x^2 − 5x − 3, 3x^3 − 5x^2 −4x − 9

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: Show that x2 + 3x + 2 has four zeros in Z6.

A:

Q: Explain the other notation which is commonly used for ak in the Newton form of the interpolating…

A: The Newton interpolation polynomial are calculated as: \

Q: Express as a polynomial. (4x - 3y)(x - 5y)

A: Given: (4x - 3y)(x - 5y)

Q: Suppose X ÷ ( – 2) is 7x? – 2x – 6 with remainder 5. - - Then X %3D

A:

Q: Formulate that the Lagrange interpolation polynomial that passes through points (0, 3), (1,4) and…

A: To show that the Lagrange interpolation polynomial that passes through points (0,-3),(1,4),(2,15) is…

Q: ) Express 8-x over Q[x] and over F2[x] as a product of irreducible ynomials.

A:

Q: 6- Show that the Polynomial has a Z4 [x] 2X+1 in multiplicative invers. in 24 [x].

A: Given

Q: Determine whether the polynomial 8+ 6x – 3x² belongs to Span{2+x – a², 1- 1, 4r²} or not.

A:

Q: Find the polynomial to represent (3x-7)2. O 9r2 - 21x + 49 O 9x2 + 21x + 49 9z2 – 42x + 49 9x2 + 42x…

A: We have to find the polynomial which represents the given expression: 3x-72 We know the algebraic…

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: Explain why 3-1 does not exist in Z24.

A: Proposition: If is element in a ring then cannot be both zero divisor and unit. Given:

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 polynomial cannot be written as the product of two other polynomials (excluding 1 and - 1),…

A: We know that a prime number have only 1 and that number as its factors.

Q: How do i find the ral seros of  a given polynomial and their corresponding multiplicities?…

A: We have to find the zeroes and their multiplicities.

Q: Show that x2 − 4 is a factor of x4 − 5x3 + 2x2 + 20x − 24.

A:

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: express f(x) =x³+2x²-x-3 , in term of lagendre polynomial

A: To express the given function f(x)=x3 +2x2 -x-3 in terms of Lagendre polynomial.

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

A:

Q: (b) Show that factorial polynomial corresponding to P,- k³ – 4k* + 2k³ – k² + k + 10 is P, = k(5) +…

A: Given: The given polynomials is Pk=k5-4k4+2k3-k2+k+10, To prove Pk=k5+11k4-k3-9k2-k1+10

Q: Show that r3 + 3x² – 8 is irreducible over Q.

A: Here Q is a field and f(x)= x³+3x²-8 is of degree 3. Then by ROOT TEST we can say that f is…

Q: Write x3 + 2x + 1 as a product of linear polynomials over someextension field of Z3.

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: Does (Z11 , + , .) have subfields? In this case which subfields.

A:

Q: Express the polynomial x3+2x+3 in Z5[x] as a product of irreducible polynomials of Z5[x] .

A: Explanation of the answer is as follows

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: Show that x2 + 3x + 2 has four zeros in Z6

A:

Q: 2. Identify the approximate input values of any relative maximums and minimums of this 5th degree…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Show that x21 + 2x8 + 1 does not have multiple zeros in anyextensionof Z3.

A:

Q: Prove that if 8x-5=-2x-15 then -x=1

A:

Q: 1. Find the sum of the polynomials: (5x°-2x+x)+(4x° – 3xª +2x³-5x) O x5 +3x4-4x3+6x O 9x5+3x4-4x³+6x…

A:

Q: Why ane absoluete value bars necelsary in the ancuees for some integrels, and not in others?…

A:

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: 19. The polynomial f(x) = (x – 2)3 = (x – 2)(x – 2)(x – 2) has æ = 2 as a zero four times. True…

A:

Q: Express as a polynomial. (3u - 1)(u + 2) + 7u(u + 1)

A: Given expression: 3u-1u+2+7uu+1

Q: Determine the upper bound on the error in the approximation – 16x5 + 256x° if |x| < 0.2 - 1+16x4

A: Given:x1+16x4 ≈x-16x5 + 256x9

Q: Which polynomial would have the following end behavior? x+ -00, f(x) - -00 x+ 0o, f(x) → -00 A y =…

A:

Q: Suppose three of the zeroes of the quintic polynomial 5x + 21x4 +74x³ + 191x² + 264x + 45 are -1/2,…

A: Given  three zeros

Q: find a quadratic polynomials whose zeores are  (i) 3,4 (ii) 2,1

A: So here we are going to use the formula for quadratic equation when zeroes are given. So I'm…

Q: Give a careful statement about the degree of the sum of two polynomials of the same degree.

A: The degree of the sum of two polynomials of same degree equals to the degree of one of the…

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

A: Solution:- Any given value is said to be upper bound for the zeros of the polynomial if all the…

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: Use Giramer Rule to Find ,z -2x + 33-Z = 1 メ+29-2-4 -2x -+7 = -3

A:

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: x2 - 4 is a factor of x4 - 5x3 + 2x2 + 20x - 24

A:

Q: Express the polynomial x3 + 2x+3 EZ[x]as a product of irreducible polynomials of 75[x]- Attach File…

A: Use the definition of irreducible polynomial and property of ring Z_5[x].