SammyS said:Gee, I think I'm still there --- or am I here ??
BTW: I've posted a couple of times in a recent Gauss's Law thread of yours.
Synthetic division is a method used to divide a polynomial by a binomial of the form (ax + b). It is a shortcut method that allows for quicker and easier division compared to traditional long division.
To perform synthetic division, the coefficients of the polynomial (9x^4 - x^2 - 6x + 2) are written in a row, with a placeholder for any missing terms. Then, the divisor (3x - 1) is written to the left of the coefficients. The first coefficient is brought down and multiplied by the divisor, and the resulting product is written below the next coefficient. This process is repeated until all coefficients have been used. The final result is the quotient of the division.
The purpose of synthetic division is to solve polynomial equations and to find the remainder when dividing polynomials. It is also useful in simplifying rational expressions and finding the roots of polynomials.
No, synthetic division can only be used when dividing by a binomial of the form (ax + b). When dividing by a polynomial with more than two terms, long division must be used.
To check the answer, the quotient obtained from synthetic division can be multiplied by the divisor and added to the remainder. The resulting expression should be equal to the original polynomial. If they are not equal, there may have been an error in the division process.