Download Unit Review 1

ALGEBRA
Review
NAME:
1. Factor each quadratic expression using a generic rectangle and a diamond problem. Clearly show all steps.
2
2
3
2
c) 4x2 – 9
a) x – 5x – 50
b) 3x + 7x – 6
d) 2x + 8x  3x  12
Check Problems
#s 1, 2, and 3
(x – 10)
5(4x + 3)
(3x – 2)
(2x – 3)
4x(2x + 3)
3  x2  2 x  5
(x + 5)
7x( x2  3x  1 )
(x + 3)
(2x  3)
(2x + 3)
(x + 4)
2x  x  7 x  2
2. Factor each expression using the GCF (Greatest Common Factor.)
2
a) 20x + 15
c) 7x3 + 21x2 – 7x
b) 8x + 12x
d) 3x2 – 6x – 15
3. Completely factor the given expression using the GCF and then a generic rectangle & diamond problem. Clearly show all steps.
a) 2x3  10x2  28x
= ____(
) = ____(
)(
)
4. For each of the following quadratic equations, solve for x using the Zero Product Property. Clearly show all steps.
a) (2x + 5)(2x – 3) = 0
c) x2 + 2x = 0
b) x² + 6x + 5 = 0
5. Use your results from problem #4 to identify the x-intercepts of the equation, then sketch each graph.
a)
y = (x + 3)(x – 1)
x-int. (
vertex (
,
,
b)
) and (
)
,
y
)
y = x² – 4x – 5
x-int. (
vertex (
,
,
)
)
and
(
,
)
y
x
x
Check Problems
#s 4 and 5
x=-5/2
x=0
x=-2
(-3, 0)
x=-5
x=3/2
(-1, -1)
(-1, -4)
(1, 0)
x=-1
(5, 0)
(2, -9)