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Use synthetic division to find the quotient and remainder when x to the 4 -24x² - 6x + 5 is divided by x-5 by completing the parts below.


(a) Complete this synthetic division table.


(b) Write your answer in the following form: Quotient +

Use synthetic division to find the quotient and remainder when x to the 4 24x² 6x 5 is divided by x 5 by completing the

Answer :

Quotient: x³

Remainder: 5

(a) To perform synthetic division, we set up the table as follows:

markdown

5 | 1 0 -24 -6 5

|___

We start by bringing down the coefficient of the highest power term, which is 1, into the bottom row:

markdown

5 | 1 0 -24 -6 5

|___

1

Next, we multiply the divisor, 5, by the value in the bottom row (1) and write the result under the next coefficient:

markdown

5 | 1 0 -24 -6 5

|___

1

-5

Then, we add the values in the second row:

5 | 1 0 -24 -6 5

|___

1

-5

---

0

We repeat the process with the new result, 0:

5 | 1 0 -24 -6 5

|___

1

-5

---

0 0

Continuing, we multiply the divisor by the value in the second row (0) and write the result under the next coefficient:

5 | 1 0 -24 -6 5

|___

1

-5

---

0 0

0

Again, we add the values in the third row:

5 | 1 0 -24 -6 5

|___

1

-5

---

0 0

0

---

0

We continue until we reach the constant term, 5:

5 | 1 0 -24 -6 5

|___

1

-5

---

0 0

0

---

0 0

0

---

5

(b) The quotient is given by the coefficients in the second row, which are 1, 0, 0, and 0. Therefore, the quotient is x³ + 0x² + 0x + 0, which simplifies to just x³.

The remainder is the value in the last row, which is 5.

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