the polynomial f(x) is given by f(x) = 2x^3 + 9x^2 + 11x - 8

Question

find the remainder when f(x) is divided by (x+2).

Answer 1

The polynomial function is and the root is - 2

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, -2. Bring the first coefficient, 2, down.

Step 3 : Multiply the first coefficient by r : (-2)(2) = 4. Write the product under the second coefficient, 9 and add : 9+(-4) =  5

Step 4 : Multiply the sum,  5, by r : (-2)(5) = -10.

Write the product under the next coefficient, 11 and add : 11+(-10) = 1.

Step 5 : Multiply the sum, 1, by r : (-2)(1) = -2.

Write the product under the next coefficient, - 8 and add : -8+(-2) = -10.

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 + 1   and remainder is -10.