Test III Math 150
Place your answers on the blank to the left. Show your work on a separate sheet.
Write your name on the upper right hand corner of this sheet. Relax and enjoy.
!b ± b 2 ! 4ac
2a
3
3
2
A ! B = ( A ! B ) A + AB + B 2
ax 2 + bx + c = 0!!!!!x =
A3 + B3
(
= ( A + B)( A
2
)
! AB + B )
2
A2 ! B2 = ( A ! B)( A + B)
Factor the Following:
________________ 1) 2y 3 ! 4y 2 + 2y 1
________________ 2) z5 ! 2z6 + z 7
________________ 3) x 2 + 19x + 18
________________ 4) y 2 + 2xy ! 15x 2
Solve the following:
____________ 5) y 2 + 2y ! 15 = 0
____________ 7) 3x 2 ! 20x + 28 = 0
2
___________ 6) x ! x ! 6 = 0
_________________8) 8x 3 ! y 6
Solve the Following:
____________ 9) One leg of a right triangle is one meter longer than the other. If the
hypotenuse is 5 meters long find the length of the other two legs.
____________ 10) A rectangular mural is 3 feet longer than it is wide. Find the
dimensions if the area is 54 square feet.
____________ 11) The length of a 200 square foot rectangular garden is twice the width.
Find the perimeter.
____________ 12) One leg of a right triangle is 2 meters longer than the other. If the
hypotenuse is 10 meters, find the lengths of the other legs.
____________ 13) The length of a rectangular garden is 1 meter greater than twice the
width. The area of the garden is 300 square meters. Find the
dimensions of the garden.
____________ 14) The cube of a number is 64 times the number. Find the number(s).
Divide the following:
__________________ 15)
x 3 ! 2x 2 ! 3x + 4
x +1
__________________ 16)
x 3 ! 27
x!3
__________________ 17)
8x 3 + 27
2x + 3