Question

G the polynomial step by step divide x cubed minus 3 x squared minus 10 x 24 by x minus 2. step 1 - fill in the missing number: a vertical line and horizontal line combine to make a l shape. there is one row of entries in the shape including 1, negative 3, negative 10, 24. on the outside to the left of the l shape is k. k = 2 step 2 - fill in the missing number: a vertical line and horizontal line combine to make a l shape. there is one row of entries in the shape including 1, negative 3, negative 10, 24. on the outside to the left of the l shape is 2 and to the outside below 1 is a. a = 1 step 3 - fill in the missing numbers: a vertical line and horizontal line combine to make a l shape. there are two rows of entries in the shape. the first row includes 1, negative 3, negative 10, 24. the second row includes blank, b, d, blank. on the outside to the left of the l shape beside row 1 is 2. on the outside below the l shape in the first column is 1 and in the second column is c. b = 2 c = -1 d = -2 complete the division. the remainder is 0. the quotient is .

Answer 1

To divide the polynomial x^3 - 3x^2 - 10x + 24 by x - 2 via synthetic division, you list the coefficients, use the divisor's root for the operation, and perform a series of multiplication and addition to get the quotient x^2 - x - 12 with no remainder.

Step-by-step explanation:

The division of the polynomial x^3 - 3x^2 - 10x + 24 by x - 2 using synthetic division is as follows:

1. Write down the coefficients of the polynomial: 1, -3, -10, 24.
2. Write the zero of the divisor, x - 2, which is 2, on the outside left of the L-shape.
3. Bring down the leading coefficient to the bottom row (1).
4. Multiply the bottom number by the zero of the divisor (2 * 1 = 2) and write this under the next coefficient (-3).
5. Add the numbers in the second column (-3 + 2 = -1).
6. Repeat the multiply-and-add process: 2 * -1 = -2, add to next coefficient (-10 + -2 = -12), and finally 2 * -12 = -24, add to the last number (24 + -24 = 0).

The final row after the division is 1, -1, -12, 0, which corresponds to the quotient x^2 - x - 12 with a remainder of 0.