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Factor completely.
1) 3x3a – 9xa2 + 18x4a
2) 300 – 3x2
3) 100y3 – 25y
4) 2x4 – 162
5) 2x2 + x – 6
6) 4x2 – 19x + 12
Solve each quadratic equation by factoring. Check all solutions. Final answers belong in a solution set
Recall: Check on your calculator by graphing the equation (once it’s equal to zero)and
looking where it crosses the x-axis!
7) x2 + 6 = 5x
8) 2x2 – 12 = 10x
9) 6x2 = x + 2
10) 6 – x2 = x
Multiple Choice: You still must show all work!
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11. Two lines are represented by the equations − 2 𝑦 = 6𝑥 + 10 and y = mx. For which value of m will the
lines be parallel?
(1) -12
(2) -3
(3) 3
(4) 12
12. What is the solution of the following system of equations? (no work here – just graphing calculator!)
y = (x + 3)2 – 4
y = 2x + 5
(1) (0,-4)
(2) (-4,0)
(3) (-4,-3) and (0,5) (4) (-3,-4) and (5,0)
13. What is an equation of the line that passes through the point (7,3) and is parallel to the line 4x + 2y = 10?
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1
1
13
(1) 𝑦 = 2 𝑥 − 2
(2) 𝑦 = − 2 𝑥 + 2
(3) 𝑦 = 2𝑥 − 11
(4) 𝑦 = −2𝑥 + 17
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14. The lines represented by the equations 𝑦 + 𝑥 = 4 and 3𝑥 + 6𝑦 = 12
2
(1) the same line
(3) perpendicular
(2) parallel
(4) neither parallel nor perpendicular
15. What is the slope of a line perpendicular to the line whose equation is 2y = -6x + 8
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1
(1) -3
(2) 6
(3) 3
(4) -6
16. What is an equation of the line that passes through the point (-2,3) and is parallel to the line whose
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equation is 𝑦 = 2 𝑥 − 4?
(1) 𝑦 =
−2
𝑥
3
(2) 𝑦 =
−2
𝑥
3
5
+3
3
(3) 𝑦 = 2 𝑥
3
(4) 𝑦 = 2 𝑥 + 6
Mark up the diagram, show all work and justifications.
17. In ∆𝐽𝐷𝐹, ̅̅̅̅
𝐹𝑇 is an angle bisector. If 𝑚∠𝐷𝐹𝐽 = 78 and 𝑚∠𝐷𝐹𝑇 = 6𝑥 − 15, find 𝑥.
Sketch & Label
Justify
Work
18. If K is the midpoint of ̅̅̅̅
𝐻𝑂, and the length of ̅̅̅̅
𝑂𝐾 is 8𝑦 + 50 and ̅̅̅̅
𝐻𝐾 is 4𝑦 + 114, find the length of ̅̅̅̅
𝐻𝑂.
Sketch & Label
Justify
Work
̅̅̅̅ = 3𝑥 + 6 and ̅̅̅̅
̅̅̅̅ is a median. If 𝐴𝑍
19. In ∆𝐴𝐵𝐶, 𝐵𝑍
𝐶𝑍 = 𝑥 + 30, find 𝑥.
Sketch & Label
Justify
Work
20. In ∆𝐴𝐶𝑇, ̅̅̅̅
𝐶𝑂 is a perpendicular bisector. If ̅̅̅̅
𝐴𝑂 = 4𝑥 + 8 and ̅̅̅̅
𝑇𝑂 = 2𝑥 + 24, and 𝑚∠𝐴𝑂𝐶 = 2𝑧 + 16, find
𝑥 & 𝑧.
Sketch & Label
Justify
Work
̅ is an altitude. If 𝑚∠𝐼𝐾𝐽 = 𝑥 + 10 and 𝑚∠𝐾𝐼𝐽 = 6𝑥 − 4, find 𝑥.
21. In ∆𝐻𝐼𝐾, 𝐼𝐽
Sketch & Label
Justify
Work
22. Lines 𝑚 and 𝑛 are parallel and are cut by transversal 𝑡. If 𝑚∠5 = 2𝑥 + 8 and 𝑚∠3 = 6𝑥 − 28, find the
measure of ∠4.
Sketch & Label
Justify
Work
23. Lines ⃡𝐴𝐵 and ⃡𝐶𝐷 intersect at point 𝑂. If ∠𝐴𝑂𝐶 = 4𝑞 + 16 and ∠𝐵𝑂𝐷 = 6𝑞 − 8, find ∠𝐶𝑂𝐵.
Sketch & Label
Justify
Work
24. Using auxiliary lines to help you solve for ∠𝐶.
Sketch & Label
Justify
25. Given the diagram on the right, prove that 𝒎∠𝒘 = 𝒎∠𝒚 + 𝒎∠𝒛.
Work
Answers:
1) 3xa(x 2 − 3a + 6x 3 )
2) 3(10 + x)(10 − x)
3) 25y(2y + 1)(2y − 1)
4) 2(x 2 + 9)(x + 3)(x − 3)
5) (2x − 3)(x + 2) (hint: the factor pair was +4 and -3)
6) (4x − 3)(x − 4) (hint: the factor pair was -16 and -3)
7) x = {2, 3}
8) x = {−1, 6}
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2
9) x = {− 2 , 3 }
10) x = {−3, 2}
11. (1)
14. (2)
12. (3)
15. (3)
13. (4)
16. (4)
#17-25 The answers below only reflect the numerical answer. It is up to you to be confident that your
justifications are correct. If you need help with any question or you are unsure of an answer, email me or
come to extra help tomorrow morning
17. 𝑥 = 9
̅̅̅̅ = 356
18. 𝐻𝑂
19. 𝑥 = 12
20. 𝑥 = 8, 𝑧 = 37
21. 𝑥 = 12
22. ∠4 = 122°
23. ∠𝐶𝑂𝐵 = 116°
24. ∠𝐶 = 89°
25.
Statement:
1) ∠𝑥 ≅ ∠𝑦
2) ∠𝑤 = ∠𝑥 + ∠𝑧
3) ∠𝑤 = ∠𝑦 + ∠𝑧
Reason:
1) Vertical angles are congruent
2) Exterior angle of a triangle = sum of two interior angles
3) Substitution Property