Algebra 2 TE: 3rd Quarter Exam Review Packet
1. Factor each expression completely.
x2 - 8x – 33
c. (x + 11) 2
d. (x - 11) (x – 3)
2. Factor each expression completely.
9x2y + 18xy2
a. CBF
b. 9x2y (1 + 2y)
c. 9xy (x + 2y)
d. 18xy (y + 2)
3. Factor each expression completely.
3x2 + 10x + 8
a. (x + 2) (x + 2)
b. (3x + 4) (x + 2)
c. (3x + 4) (3x – 2) d. 3x(x+2) + 4(x+2)
4. Factor each expression completely.
x2 + 5x - 15
a. (x + 15) (x – 1) b. (x + 3) (x – 5)
c. (x + 5) (x – 15)
a. (x – 11) (x + 3)
b. (x + 11) (x – 3)
5. Solve by factoring.4x2 + 17x – 42 = 0
2
a.
b. –6, 4
6, 
3
6. Solve by factoring.
4x2 + 27x – 40 = 0
a. –8, 4
b. 5
4
, 
1
2
c.
c.
–6,
8, 
1
2
d. CBF
7
d. 7
4
4
d.
–8,
, 
5
4
2
3
Solve the equation by finding square roots.
7. 2x2 = 18
a. 3
b.
√18
±
2
c. −√9, √18
d. ± 3
8. 3x2 = 33
a.
11
b.
√33
±
3
c. ±√11
d. −√11, √33
9. The function y = -16t2 + 404 models the height y in feet of a stone t seconds after it is dropped
from the edge of a vertical cliff. How long will it take the stone to hit the ground? Round to the
nearest hundredth of a second.
a. 10.05 seconds
c. 5.02 seconds
b. 7.11 seconds
d. 0.25 seconds
10. Simplify √−75 using the imaginary number i.
a. 5√−3
b. 𝑖√75
c. −5√3
d. 5𝑖√3
11. Simplify √−32 using the imaginary number i.
a. 4𝑖√2
b. 4√−2
c. 𝑖√32
d. −4√2
Write the number in the form a + bi.
12. √−9 + 8
a. 9 + 8i
b. 8 + i√9
c. 8 + 3i
d. 3 + 8i
13. 1 − √−175
a. −1 − 5𝑖√7
b. 1 − 5𝑖√7
c. −1 + 𝑖√175
d. 1 + 5𝑖√7
Simplify the expression.
14. (-6 – 2i) + (2 – i)
a. -8 + i
b. -4 – 3i
c. -7i
d. 4 + 3i
15. (3 + 5i) – (6 – i)
a. 3i
b. 3 – 6i
c. 9 + 4i
d. -3 + 6i
16. (-5i)(3i)
a. 15
17. (5 – 6i)(4 + 5i)
a. -10 + i
b. 20 – 30i
b. –15
c. 15i
c. 50 + i
d. 20 + i
18. Solve the equation by square roots, 9x2 + 25 = 0
a. ± 5 𝑖
c. ± 3 𝑖
5
3
b. ± 5
d. ± 25 𝑖
3
9
d. –15i
19. Solve the equation by factoring, x2 + 6x + 9 = 49
a. 10, –4
c. 4, –10
b. 4, –4
d. 10, –10
Use the Quadratic Formula to solve the equation.
20.
–x2 + 5x – 4= 0
21.
3x2 + 5x + 7 = 0
22. A landscaper is designing a flower garden in the shape of a trapezoid. She wants the shorter
base to be 3 yards greater than the height and the longer base to be 7 yards greater than the
height. She wants the area to be 300 square yards. The situation is modeled by the equation
h2 + 5h = 300. Use the Quadratic Formula to find the height that will give the desired area.
Round to the nearest hundredth of a yard.
a. 610 yards
c. 15 yards
b. 17.5 yards
d. 30 yards
23. Classify –4x4 – 3x2 by degree and by number of terms.
a. quintic binomial
c. quintic trinomial
b. quartic binomial
d. quartic trinomial
24. Classify –5x5 – 8x4 – 2x3 by degree and by number of terms.
a. cubic binomial
c. quartic trinomial
b. quintic trinomial
d. quadratic binomial
25. Zach wrote the formula w(w – 1)(2w + 3) for the volume of a rectangular prism he is designing,
with width w, which is always has a positive value greater than 1. Find the product and then
classify this polynomial by degree and by number of terms.
26. Write 2x2(3x2 – 5x3) in standard form. Then classify it by degree and number of terms.
a. –10x5 – 15x4; quartic binomial
c. –10x5 + 6x4; quintic binomial
b. 5x5 + 6x4; quintic trinomial
d. 5x – 3x4; quintic binomial
27. Write the expression (x + 6)(x – 3) as a polynomial in standard form.
a. x2 + 9x – 9
c. x2 + 9x – 18
b. x2 – 9x + 3
d. x2 + 3x – 18
28. Write the expression (x + 5)(x – 3) as a polynomial in standard form.
a. x2 + 2x – 15
c. x2 – 8x + 2
b. x2 + 8x – 15
d. x2 + 8x – 8
29. Write 2x3 + 8x2 – 24x in factored form.
a. 2x(x – 2)(x – 6)
c. 6x(x – 2)(x + 2)
b. –2x(x + 2)(x + 6)
d. 2x(x + 6)(x – 2)
30. Use a graphing calculator to find the relative minimum, relative maximum, and zeros of
y= x3 + 16x2 – 10x – 30. If necessary, round to the nearest hundredth.