Synthetic Division and the Remainder Theorem Answers

Identify all of the roots of the function.f(x) = x3 – 5x2 – 2x + 24

The completely factored form of the polynomial is f(x) = (x – 5)(x – 2)(x – 4)(x – 5)(x + 2)(x + 4)(x – 5)(x2 + 6x + 8).

c =

d =

Complete the division. The remainder is 0.The quotient is .

Complete the steps to factor the polynomial.One root of f(x) = x³ + x² - 22x - 40 is 5. If 5 is a root of the function, then is a factor.

Complete the steps to factor the polynomial.One root of f(x) = x³ + x² - 22x - 40 is 5. If 5 is a root of the function, then is a factor.

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 =

Look at the work shown for the division problem shown on the right. The remainder is .

Identify all of the roots of the function.f(x) = x3 – 5x2 – 2x + 24

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 =

Now, evaluate f (x) = 2x4 – 4x3 – 11x2 + 3x – 6 for x = –2.f (–2) =

Compare the values you entered above.f (–2) is the remainder when dividing the polynomial by x + 2.

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 =