Polynomial Long Division : Linear Divisor

Related BrainMass Solutions

• Factor polynomial

  Find the quotient by long division using as the divisor ? Find the other two linear factors (do not use long division) ?

• Synthetic division,Remainder factor theorem, graphing cubic

  Synthetic division is a shortcut method for dividing a polynomial by a linear factor of the form x + a or x - a. Synthetic division can also be used in conjunction with the "Remainder Theorem" to find the value of a polynomial at a real value.

• Synthetic Division and Polynomials

  In synthetic division, what relationship does the divisor and remainder have to the original polynomial function, according to the Remainder Theorem? 2.

• product of a linear and cubic factor

  (i) The Remainder Theorem tells us that the remainder of a polynomial f(x) divided by a linear divisor x-c is equal to f(c). We have f(x)=9x^5-4x^4 divided by 3x-1=3(x-1⁄3).

• improper rational function

  Express the improper rational function as the sum of a polynomial and a proper rational function: This can be done using long division. .

• Irreducible over the rationals.

  † , i.e., is not a divisor of , , , but † , i.e., is not a divisor of .

• Elliptic Curves

  Write down the division polynomial (psi_3)(x) for this curve. 2. Show that the greatest common divisor of (psi_3)(x) and "x^5 -x" is "x(x-1)." 3. Use part (2) to show that the 3-torsion points in E(F5) are {Origin,(0,1),(0,-1)}."

• Application of Long Division

  This is now a real life problem where we need to perform long division. The dividend is x^2 + 2x + 3 and the divisor is 3x - 4. The application of long division is determined.

• Find real and imaginary roots

  The solution shows how to use synthetic division and solving of a quadratic equation to find the remaining roots of a polynomial.