Alg1A/GeomA – Chapter 10 Review Sheet
Name:
Factoring and Solving Quadratic Equations
Date: Per:
Part I. Factor completely: (If not factorable, provide sufficient evidence)
1.
x + 5x − 6
2.
5.
12x y + 15x y − 21x y 32x 2 − 80x + 50
3x 2 + 75
2
4. 3 3
3.
2x − 3x − 20
2
2
4
4
6
5x − 13x + 6 2
6.
7.
8.
9.
x + 6x + 10
4x − 100
2
2
2x 2 − 8x − 42
10.
11.
25x − 16y 2
12.
x + x − 4x − 4 3
2
2
a 2 − 11ab + 18b 2
13.
14.
16 − 81x
4
15.
x + x y − xy − y 3
2
2
3
6x 2 + x − 15
Part II. Solve each equation by factoring. If the equation can’t be factored, solve using the quadratic formula.
1.
2.
0 = x 2 − 8x + 12
4.
3.
x 2 − 4x − 4 = 0
3x 2 = 10x
5.
x − 4x = −6 2
2x 2 + 3 = −8x
6.
x + 16 = −8x 2
7.
8.
9.
x = 8x
3x + 6 = 11x 2
2
8x 2 + 10x − 3 = 0
10.
11.
x = −4 2
2x 2 − 7x + 5 = 0
12.
x − 10x = 0 2
13.
14.
15. 2
4x = 20x − 25
15x − 12 = 3x
2
4x 2 = 4x + 1
Part III. Find the sum, difference, or product of the following polynomials.
1.
(5x
2
2.
)
(x
− 9x + 1 − (8x + 13)
2
) (
− 3x − 1 + 5x + 2 2
3.
)
(x − 3)(2x − 3)
4.
(
2x − 3x 2 − 4 x + 2
(2x
2
)
)
− 3x − 4 (4x + 3)
5.
6.
(5x − 2 )
2
For each of the following functions, find (a) the xintercepts by factoring, (b) the vertex, and (c) sketch a graph
7.
8.
y = x + 6x + 8 2
9.
y = x − 4x − 5 2
y = x2 − 4
Vertical Motion Model:
10. From a balcony 64 feet above the ground, you throw a ball upward with an initial velocity of 48 feet per second.
a.
Write the equation that describes the vertical motion of the ball.
b.
How long will it take for the ball to reach the ground? (solve by factoring)
c.
How high is the highest point in the ball’s flight?