Step-by-step explanation:
Absolutely! Synthetic division is a method used to divide polynomials, making the process easier and quicker compared to long division.
Here's a simple step-by-step breakdown:
1. **Set up the division:** If you're dividing \(ax^3 + bx^2 + cx + d\) by \(x - r\), where \(r\) is a root of the polynomial (which means \(r\) makes the polynomial equation equal to zero), arrange the coefficients of the polynomial.
2. **Write down the coefficients:** Take the coefficients of \(x^3, x^2, x,\) and the constant term (if any) of the polynomial, and write them in order.
3. **Start dividing:** Using synthetic division involves a simple process:
a. Write the root value \(r\) outside a division box.
b. Copy down the first coefficient (of \(x^3\)) underneath the division box.
c. Multiply the value outside the box (root \(r\)) by the number you've just written down and write the result below the next coefficient.
d. Add vertically, then repeat the process until you've gone through all the coefficients.
e. The final numbers at the bottom row of the division box are the coefficients of the quotient (except for the remainder, if there is one). The last number is the remainder.
Would you like to try an example or need further clarification on any step?
