algebra study guide 12

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