complete attachment with solving the problem and the answer

No Work ⇔ No Points

Use Pencil Only ⇔ Be Neat & Organized

1. (2 points) Use synthetic division to show 1 is a solution of 4×2 − 3x − 1 = 0.

1.

2. (3 points) Use synthetic division to show −2 is a solution of x3 + 6×2 + 12x + 8 = 0.

2.

3. (4 points) Use synthetic division to show x + 3 and x − 4 are factors of

p(x) = 2×3 + x2 − 27x − 36, then write p(x) in factored form.

3.

Page 1 of 4

Study Guide 12

Total Points: 50

4. (4 points) Use synthetic division to show 3x + 1 is a repeated factor of

p(x) = 9×3 − 39×2 − 29x − 5, then write p(x) in factored form.

4.

5. Find a second degree polynomial equation p(x) = ax2 + bx + c, with the given zeros

below:

1

(a) (3 points) −5 and

2

(a)

(b) (3 points) ±4i

(b)

(c) (4 points) −5 ± 3i

(c)

√

(d) (4 points) 2 ± 5

(d)

Page 2 of 4

Study Guide 12

Total Points: 50

6. Find a third degree polynomial equation p(x) = ax3 + bx2 + cx + d, with the given

zeros below:

−1

(a) (3 points) − 5, 1, and

2

(a)

2

(b) (3 points) ± , and 2

3

(b)

(c) (4 points) 3 ± 4i, and −2

(c)

Page 3 of 4

Study Guide 12

Total Points: 50

7. Consider the graph below:

9

8

7

6

5

4

3

2

1

-5

-4

-3

-2

0

-1

0

-1

1

2

3

4

5

-2

-3

-4

-5

(a) (3 points) What are the x-intercepts of this graph?

(a)

(b) (2 points) What is the y-intercept of this graph?

(b)

(c) (5 points) Find a third degree polynomial equation p(x) = ax3 + bx2 + cx + d

for the graph displayed above.

(c)

(d) (3 points) Find the interval where p(x) ≥ 0.

(d)

Page 4 of 4

Study Guide 12

Total Points: 50