Review Problems1. Write each complex number in standard form a +bi.

(a) (1 – 3i) + (7 — 4i)

(b)

(5 – 3i) – (2 + 7i)

–

(c) (5 + 3i) · (2 + 7i)

(e)

1

(d)

3 + 4i

(g) (2+i)3

1+ 4i

2 – 3i

(f)

-2 V-54

4

2. Find all solutions (real and complex)

(a) x2 + 25 = 0

(b) x2 – 4x = -8

(C) 3×2 + 5 = -41

3. Find all real solutions for x and simplify your answers:

х

(a) 2×2 = 6 – x

=

1

2x + 1

(b) +

X – 2

x + 3

x2 + x – 6

(d) x4

8×2 – 9= 0

(c) x2 + 2x – 2 = 0

–

(e) –5 = x + V x + 17

(g) (2x – 1)1/3 = 2

(i) 7 – 4(x + 2) = 3x + 5

=

(f) 23 + 2×2 – 3x — 6 = 0

(h) x6 + 3×3 – 40 = 0)

(i) 4x + 71 = 19

=

=

4. Simplify each of the following. Write any polynomials in standard form.

1

2

2

(a)

(b)

(c) 5×2 – X – 3(x − 2)2

—

2

+1

१२ |

х

x3 + 8

x² – 4

(d) 5(x + 1)3

(e)

(f)

x2

x2 – X – 6

X + 2

x6

(g)

(x – 5) + 7

(x – 5)(x + 2)

5. Factor completely:

(a) 9×2 – 25y2

(d) y3 + 2y2 – 9y – 18

(g) 8×2 – 14x 15

(b) x4 + 3×2 – 4

(c) a} – 2763

(e) 4a² (3x – 1) – 9(3x – 1) (f) 27×3 + 1

=

2

6. Let f(x) = 174 and g(x) = x2 – 3. Find and simplify:

(a) (fog)(x) (b) (gof)(2) (c) g(x+h)

(e) (909) (2) (f) -(0)

(g) f(-1)

(0) (-9) ()

(d) f-1(x)

(h) (f.g) (2)

7. Consider the quadratic function f(x) = –2×2 – 8x + 10.

(a) Write in form y =

= a(x – h)2 + k. (b) Find the vertex.

(c) Find the y-intercept.

(d) Find any x-intercept(s).

8. Solve each of the following. Write your answer in interval notation.

3.0

(a) -7

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