Lesson 4.6: Synthetic Division and the Remainder Theorem Answers

Step 3 - Fill in the missing numbers:b =

c =

d =

Divide [image 1] by [image 2] .Step 1 - Fill in the missing number: [image 3] k = ⇒ 2

Complete the division. The remainder is 0.The quotient is ✔ x² - x - 12X -x² + x + 1212x² - x - 112x² + x + 1.

Now, evaluate f (x) = 2x4 – 4x3 – 11x2 + 3x – 6 for x = –2.f (–2) = ⇒ 8

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 X -55✔ x - 5x + 5 is a factor.

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

Look at the work shown for the division problem shown on the right. The remainder is ⇒ 8.

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

Compare the values you entered above.f (–2) is less than✔ equal toX greater than the remainder when dividing the polynomial by x + 2.

The result of dividing (x3 + x2 – 22x – 40) by (x – 5) is x2 + 6x + 8. Select all of the factor(s) of x2 + 6x + 8.

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