Question

Use division to prove that x=11 is a real zero of y=-x^3+12x^2-39x+308

Answer 1

The polynomial function

Use synthatic division to find

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 at the right.

Step - 2:

Write the constant r of the divisor (x - r) to the left. In this case, r = 11. Bring the first coefficient -1, down.

Step - 3:

Multiply the first coefficient by r : 11*-1 = - 11.

Write the product under the second coefficient, 12 and : 12 + (- 11) = 1.

Step - 4:

Multiply the sum, 1, by r : 11*1 = 11.

Write the product under the next coefficient, -39 and add : -39 + 11 = -28.

Step -  5:

Multiply the sum,-28, by r : 11*-28 = 308 .

Write the product under the next coefficient, 308 and add : 308 + (- 308) = 0. The remainder is 0.

Therfore, x = 11 is a real zero of .