# Use synthetic division to find the quotient and the remainder.

Given P(x) = 2x3 - 11x2 + 18x - 15 is divided by x – 3. Use synthetic division to find the quotient and the remainder.
 A. 2x2 + 3x + 2; 0 B. 2x2 – 5x + 3; –6 C. 2x2 – 3x; –2 D. 2x2 + 3x – 2; 0

The function is 2x3 - 11x2 + 18x - 15, and the root is 3.

Step 1 : Write the terms of the dividend so that the degrees of the terms are in descending order. Then write just the coefficients as shown below.

Step 2 : Write the constant r of the divisor (x - r) to the left. In this case, 3. Bring the first coefficient, 2, down.

Step 3 : Multiply the first coefficient by r : (3)(2) = 6. Write the product under the second coefficient, - 11 and add :

-11+(6) = - 5

Step 4 : Multiply the sum, - 5, by r : (3)(-5)=-15.

Write the product under the next coefficient, 18 and add : 18+(-15) = 3.

Step 5 : Multiply the sum, 3, by r : (3)(3) = 9.

Write the product under the next coefficient, - 15 and add : -15+(9) = -6.

The numbers along the bottom row are the coefficients of the quotient. Start with the power of x that is one less than the degree of the dividend.

Thus, the quotient is 2x²-5x+3   and remainder is -6.

So option B is correct.