(a) Calculate the resultant of A = 3x² +3 and B = (x-2)(x+5) by hand. (b) Let A, B, C be non-constant polynomials in R[z]. Show that res(A, BC) = res(A, B).res(A,C).

Q: 2xy// + (x + 1)y/ +3y = 0

A:

Q: Find the third Maclaurin polynomial to f(x) = e sinx

A: The Maclaurin series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where the center is at x=a=0…

Q: Express the polynomial a+ 3 +a2 + 2r as a product of its irreducible factors in Z,lr).

A:

Q: 1. Determine a possible equation for each polynomial function. a) f(x)= d) f (x) = c) f(x) = f) f…

A: To find the equation of the given graph of function f(x) :-

Q: Find the linear polynomial p(x) = a1x + ao, that interpolates the two points with coordinates (3, 0)…

A: Given query is to find the equation of the line.

Q: Which statement is NOT true? When using the conv command, the two polynomials have to be of the…

A: consider the equation

Q: Use appropriate Lagrange interpolating polynomials to approximate f(1) if f(0) = 0, f(2) = −1, f(3)…

A:

Q: The coordinates of the P(x)=x³ – 2x2 + 3x polynomial with respect to the base B-[1, x, x?,x'] are as…

A:

Q: Let F = (, , 2). Calculate div (F) and curl (F). (Use symbolic notation and fractions where needed.)…

A: We have to calculate  and .

Q: 2. Is the following set of polynomials linearly independent in P2? Explain your work. (-1+2t + 3t?),…

A:

Q: Express the polynomial x5 + 3x3 + x2 + 2x as a product of its irreducible factors in Z5[x].

A: Given: [May be the question is wrong, otherwise the given solution is correct.] The given polynomial…

Q: Does the following set of polynomials {t? + 1, t2 + t,t + 1} span P2?

A:

Q: Find all non-negative integer pairs of (x, y) such that (xy-7)² = x² + y²

A: Find all non-negative integer pairs of (x, y) such that .

Q: Find curl (82 i + 9x j + 6y k). curl (82 i + 9x j + 6y k) = = ( )k )i + (i )j + (

A: To Find : curl(8z i + 9x j +6y k)

Q: Find Ao, A1, and Az in rewriting the function of f(x=2vx 0マx in terms of Lagure polynomial ョーの

A: Given: Let us consider the given function  fx=2x       x≥00             x<0 and the Lagure…

Q: Let f(r) be a polynomial function such that f"(x) = xª – 5z + 6z². Find the æ values for the…

A:

Q: Are the polynomials x? + 1,x? – 1, 2x – 1 linearly independent in P2?

A:

Q: Consider the function f(x)=x+2x.f(x)=x+2x. Construct the Lagrange interpolation polynomial which…

A: Lagrange's interpolation formula for n points can be defined as:…

Q: Q3: Factorize f (x) = 2x* + x³ + 2x + 4 € Z5[x] as a polynomials product to irreducible over Z5?

A:

Q: Consider the polynomials a(x) = r' + x³ + x + 4 and b(x) = 2r³ + 4.x² + x + 2 from Z5[r]. a) Find…

A:

Q: 2j(5-j3) B) Given that (2a+jb)+(b-j3a)=- Obtain the values of a and b. (2+j)(1+j4)

A: Solve the left and right-hand side independently left-hand side 2ab+3ab+jb2-6a2 5ab+jb2-6a2…

Q: Evaluate (521 + 3z2)

A:

Q: 1 using the divided-differences method. Consider the function f(x) =, rE-1,1]. Construct the…

A: Given function is fx=21+x2, x∈-1,1. We have to construct the interpolation polynomial which…

Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ |

A: find the polynomial f(x) for which  x fx-1=x-3 fx ∀x for x=0 x fx-1=x-3 fx ∀x

Q: [7 0] Consider A = 5 7 and find AA" and ATA and AA"A or explain why these products do not exist.

A:

Q: Let f = {(1,-1), (4,-2), (9,-3), (16,4)} and g = {(-1,-2), (-2, -4), (-3,-6), (4,8)}. Show that gof…

A:

Q: (b) Are the polynomials x + 5, x – 5, 2x +1 linearly independent in P1(R)? Explain.

A: The vectors a1, ..., an are called linearly independent if there are no non-trivial combination of…

Q: 2. (a) Define the dot product of two polynomials p(x) = ao+a₁x+a₂x²+a3x³ and q(x) = bo+b₁x+b₂x²+b3x³…

A:

Q: For the polynomial below, 1 is a zero. h(x) =x- 7x + 10x- 4 x=(x)4 Express h (x) as a product of…

A:

Q: Let f(x) = , find L, (x) of the second Lagrange interpolating polynomial, if x, =2, x, =2.5, X2 =4…

A: Find second order Lagrange interpolation polynomial

Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: Find the splitting field for f (x) = (x2 + x + 2)(x2 + 2x + 2) overZ3[x]. Write f (x) as a product…

A: Given: fx=x2+x+2x2+2x+2. We have to find the splitting field of f(x) over Z3x.Also, write f(x) as a…

Q: Let f(x) = x3+5x+3. Construct the divided-difference table based on the nodes x0= 1, x1 = 2, x2 = 3,…

A: