Algebra Worksheet 6, Group 1
1. Multiply the following polynomials, and then simplify your answer.
(a) 5x4(2x3 - 3x2 + 1)
(b) (2x + 5)(3x - 4)
(c) (x2 - 4x)(3x - 5)
(d) (x + 2)2
(e) (x - 4)(x + 4)(x + 1)
(f) (x - 1)3
2. Factor the following polynomials:
(a) 3x4 + 6x2
(b) 5x2 - 25x
(c) x2 + 9x + 20
(b) x2 + 10x + 21
(e) x2 - 2x - 15
(f) x2 - 6x + 8
(g) x3 + 7x2 + 12x
(h) x3 - 11x2 + 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) (x2 - 9)(x + 4) = 0
(d) x2 + 13x + 42 = 0
(e) x2 - 7x + 12 = 0
(f) x3 - 5x2 + 6x = 0
(g) x2 - x = 6
(h) x2 = 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) 2x2 + 3x - 5 = 0
(b) 3x2 - 5x - 2 = 0
c) x2 + 3x + 1 = 0
(d) 2x2 - 6x + 3 = 0
(e) 5x2 + 6x = 3
(f) 4x2 = 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 = -16t2 + 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.
