The values of a, A, B, C for which the quadrature formula Ca-x)f(x)dx = Af(-a) + Bf(0) + Cf(a) %3D is exact for polynomials of highest possible degree, are:

Q: Find the value of “a” if (x1/3)(x3/4) = xa

A: Use Formula  (xm)(xn) = x(m+n)  When the two terms are in Multiplication and their bases are same…

Q: Find the value of c that will cause the polynomial f(x) = x2 + 3x + c to have 3 as

A: f(x)=x2+3x+c

Q: Find all the factors of f (x) = x³ – 4x² + x + 6.

A: GIVEN: f(x) = x3 - 4x2 + x + 6

Q: f(x) = √√x and g(x) = x² − 4x, find the following and their domains:

A: Given function:- fx=x and gx=x2-4x

Q: Given roots x = 4 (multiplicty 2), x = 1 + sqrt(2), and a leading coefficient of 1, write a…

A: Given:   Roots of polynomial: x = 4 (with multiplicity 2)  and  x = 1 + 2 Therefore other root is x…

Q: Find a polynomial of the form 3 2 f(x) = ax° + bx + cx + d such that f(0) = -2, f(-2) = -5, f(-3) =…

A: We have to solve given problems:

Q: The base of a triangle is (x + 7) cm and its height is (x - 3). Which of the following polynomial…

A:

Q: Determine the following for the function f(x)=4x3+4x2-x-1 a) the end behavior of the function  b)…

A: Interpretation:a.The given polynomial function is f(x) = 4x3+4x2-x-1.Since the leading coefficient…

Q: 2) Show that a3 + b³ = (a + b)(a² – ab + b²) is a polynomial identity. %3D |

A: Start with Right hand side as follows.

Q: Find the roots of the polynomial: f (x) = 2(x – 5)³ + 16.

A: Given f(x)=2x-53+16

Q: Determine the roots of the function f(x) = (52" – 6)² – (5²" – 6) – 12. -

A:

Q: Determine the 3rd degree polynomial which passes through the following points: 3 1 1 7 y 25

A:

Q: Find Ao, A1, and 4, in rewriting the function of ()- r>0 in terms of Lagure polynomial, /)=4L(*).

A:

Q: Calculate the roots of the following polynomial equations: (a) x – 6x2 + 1lx – 6 = 0 given x = 1 is…

A: