6. Divide $$ x^{3}-16 x^{2}+15 x+10 $$ by $$ (x-2) $$. a. $$ x^{2}-18 x+43, \mathrm{R} 36 $$ c. $$ -x^{2}+14 x+13 $$ b. $$ -x^{2}+18 x-43 $$ d. $$ x^{2}-14 x-13, \mathrm{R}-16 $$ 7. Divide $$ -8 x^{3}+940+12 x $$ by $$ (x-5) $$. a. $$ -8 x^{2}-40 x-188 $$ c. $$ 8 x^{2}+40 x+188 $$ b. $$ -8 x^{2}+40 x+212 $$, R 1880 d. $$ 8 x^{2}-40 x-212, \mathrm{R}-1880 $$ 8. Use synthetic division to find $$ P(2) $$ for $$ P(x)=x^{4}-8 x^{3}+9 x^{2}+5 x+8 $$. a. 2 b. 6 c. 22 d. 26 9. Use synthetic division to find $$ P(-4) $$ for $$ P(x)=x^{4}+7 x^{3}+5 x+4 $$. a. -4 b. -208 c. 720 d. -48

Question

UpStudy AI · Accepted Answer

Let's solve each problem step by step and identify the correct answers from the provided options.

---

### **6. Divide $$ x^{3} - 16x^{2} + 15x + 10 $$ by $$ (x - 2) $$.**

**Using Synthetic Division:**

1. **Set Up:**
   - Divisor root: $$ x = 2 $$
   - Coefficients: $$ 1 $$ (for $$ x^3 $$), $$ -16 $$ (for $$ x^2 $$), $$ 15 $$ (for $$ x $$), and $$ 10 $$ (constant term).

2. **Process:**
   ```
   2 |  1   -16    15    10
       |        2    -28   -26
       --------------------------
          1   -14    -13    -16
   ```
   
3. **Result:**
   - **Quotient:** $$ x^{2} - 14x - 13 $$
   - **Remainder:** $$ -16 $$

**Correct Option:**  
**d. $$ x^{2} - 14x - 13, \mathrm{R} -16 $$**

---

### **7. Divide $$ -8x^{3} + 12x + 940 $$ by $$ (x - 5) $$.**

**Using Synthetic Division:**

1. **Set Up:**
   - Divisor root: $$ x = 5 $$
   - Coefficients: $$ -8 $$ (for $$ x^3 $$), $$ 0 $$ (for $$ x^2 $$), $$ 12 $$ (for $$ x $$), and $$ 940 $$ (constant term).

2. **Process:**
   ```
   5 |  -8     0      12      940
       |         -40    -200    -940
       ------------------------------
           -8    -40    -188        0
   ```
   
3. **Result:**
   - **Quotient:** $$ -8x^{2} - 40x - 188 $$
   - **Remainder:** $$ 0 $$

**Correct Option:**  
**a. $$ -8x^{2} - 40x - 188 $$**

---

### **8. Use synthetic division to find $$ P(2) $$ for $$ P(x) = x^{4} - 8x^{3} + 9x^{2} + 5x + 8 $$.**

**Using Synthetic Division:**

1. **Set Up:**
   - Value to evaluate: $$ x = 2 $$
   - Coefficients: $$ 1 $$ (for $$ x^4 $$), $$ -8 $$ (for $$ x^3 $$), $$ 9 $$ (for $$ x^2 $$), $$ 5 $$ (for $$ x $$), and $$ 8 $$ (constant term).

2. **Process:**
   ```
   2 |  1    -8     9      5      8
       |        2    -12    -6     -2
       ------------------------------
           1    -6    -3     -1      6
   ```
   
3. **Result:**
   - **$$ P(2) = 6 $$**

**Correct Option:**  
**b. 6**

---

### **9. Use synthetic division to find $$ P(-4) $$ for $$ P(x) = x^{4} + 7x^{3} + 5x + 4 $$.**

**Note:** The polynomial $$ P(x) $$ is missing the $$ x^{2} $$ term. It can be rewritten as $$ P(x) = x^{4} + 7x^{3} + 0x^{2} + 5x + 4 $$.

**Using Synthetic Division:**

1. **Set Up:**
   - Value to evaluate: $$ x = -4 $$
   - Coefficients: $$ 1 $$ (for $$ x^4 $$), $$ 7 $$ (for $$ x^3 $$), $$ 0 $$ (for $$ x^2 $$), $$ 5 $$ (for $$ x $$), and $$ 4 $$ (constant term).

2. **Process:**
   ```
   -4 |  1      7       0       5        4
           |        -4     12     -48      188
       ---------------------------------------
             1      3      12      -43      192
   ```
   *(Note: There seems to be a miscalculation here. Let's correct it.)*

**Correct Process:**
   ```
   -4 |  1      7       0        5         4
           |        -4     -12      48      -212
       -----------------------------------------
             1      3     -12       53      -208
   ```
   
3. **Result:**
   - **$$ P(-4) = -208 $$**

**Correct Option:**  
**b. -208**

---

**Summary of Correct Answers:**

- **Question 6:** **d**
- **Question 7:** **a**
- **Question 8:** **b**
- **Question 9:** **b**
**Correct Answers:** - **6.** d - **7.** a - **8.** b - **9.** b

Divide by .
a.
c.
b.
d.

Divide by .
a.
c.
b. , R 1880
d.

Use synthetic division to find for .
a. 2
b. 6
c. 22
d. 26

Use synthetic division to find for .
a. -4
b. -208
c. 720
d. -48

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions

Divide by . a. c. b. d. Divide by . a. c. b. , R 1880 d. Use synthetic division to find for . a. 2 b. 6 c. 22 d. 26 Use synthetic division to find for . a. -4 b. -208 c. 720 d. -48

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Algebra Questions

Divide by .
a.
c.
b.
d.

Divide by .
a.
c.
b. , R 1880
d.

Use synthetic division to find for .
a. 2
b. 6
c. 22
d. 26

Use synthetic division to find for .
a. -4
b. -208
c. 720
d. -48