Final answer:
To divide using synthetic division, set up the division in the synthetic division format, find a zero of the binomial, and then use synthetic division to divide the polynomial by the binomial using the zero. The quotient is the result of synthetic division.
Step-by-step explanation:
To divide using synthetic division, we will start by setting up the division in the synthetic division format. The given polynomial is 9x³−6x² and we want to divide it by the binomial x−2x+2.
x² + 2x - 3
Next, we will find a zero of the binomial x−2x+2 by setting it equal to zero and solving for x. x−2x+2 = 0. Simplifying, we get x² + 2x - 3 = 0. Solving this quadratic equation, we find that the zero of the binomial is x = 1.
Using synthetic division, we will divide the polynomial by the binomial using the zero we found. The coefficients of the polynomial are 9, -6, and 0 (since there is no x term). The result of synthetic division is the quotient:
9x² + 20x + 40