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 = -3 ⇒ 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 = 24 ⇒ 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 = c = d =

In the case of dividing by a linear factor, the synthetic division is a shorthand, or quicker, a technique of polynomial division.

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We have a polynomial:

x³ - 3x² - 10x + 24

Which is divided by (x - 2)

We can divide using the synthetic division:

The first row: 1 -3 -10 24

The entry outside the row: 2

The missing value which is 2

k = 2

Thus, the value of k is 2 if the polynomial x³ - 3x² - 10x + 24 is divided by the expression (x - 2).

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