1. Multiply the following polynomials, and then simplify your answer.

(a) 5x^{4}(2x^{3} - 3x^{2} + 1)

(b) (2x + 5)(3x - 4)

(c) (x^{2} - 4x)(3x - 5)

(d) (x + 2)^{2}

(e) (x - 4)(x + 4)(x + 1)

(f) (x - 1)^{3}

2. Factor the following polynomials:

(a) 3x^{4} + 6x^{2}

(b) 5x^{2} - 25x

(c) x^{2} + 9x + 20

(b) x^{2} + 10x + 21

(e) x^{2} - 2x - 15

(f) x^{2} - 6x + 8

(g) x^{3} + 7x^{2} + 12x

(h) x^{3} - 11x^{2} + 30x

3. Solve the following equations. (You do not need to use
the quadratic formula for these

problems.)

(a) (x + 1)(x - 2) = 0

(b) (2x + 3)(3x - 9) = 0

(c) (x^{2} - 9)(x + 4) = 0

(d) x^{2} + 13x + 42 = 0

(e) x^{2} - 7x + 12 = 0

(f) x^{3} - 5x^{2} + 6x = 0

(g) x^{2} - x = 6

(h) x^{2} = 9x - 20

4. Recall that the quadratic formula is:

Use the quadratic formula to solve the following
equations. When the answers are not

integers, give your answer as a decimal to two decimal places.

(a) 2x^{2} + 3x - 5 = 0

(b) 3x^{2} - 5x - 2 = 0

c) x^{2} + 3x + 1 = 0

(d) 2x^{2} - 6x + 3 = 0

(e) 5x^{2} + 6x = 3

(f) 4x^{2} = 3x + 5

5. Susan is one year older than Bob. The product of their ages is 306. What is Bob's age?

6. A ball is thrown directly upward with a velocity of 96
feet/second. The height of the ball

after t seconds is given by the following equation:

h = -16t^{2} + 96t

The maximum height attained by the ball is 144 feet. When is the ball at this height?

7. A garden measuring 12 meters by 16 meters is to have a
pedestrian pathway (with width

x) installed all around it, increasing the total area to 285 square meters.
Determine the

width of the pathway.