8-A2
Algebra 1H
Factoring Trinomials
Name__________________
(when the Leading Coefficient is 1) Lesson 8-3
Factor each trinomial. Check by multiplying the factors using FOIL. If the
polynomial is not factorable, write PRIME.
1. y2 + 7y + 12
2. x2 + 12x - 48
3. x2 – 11xy + 18y2
4. x2 + 4xy – 45y2
5. x2 - x - 30
6. x2 – 15x + 35
7. x2 + 3xy – 54y2
8. y2 - 5y - 14
9. x2 - 9x + 14
10. 30 - 17x + x2
11. x2 + 4xy – 21y2
12. a2 + 19ab + 60b2
Ch 8 Handouts Alg 1H
Define:
13.
Prime Numbers: _________________________________________
Composite Numbers: _____________________________________
14.
When factoring out the greatest common monomial factor your answer
will be the __________ of the ________ and the remaining factors.
15. A polynomial can be factored by grouping if all of the following are true:
(a) ____________________________________________________
(b) ____________________________________________________
(c) ____________________________________________________
Factor. Check by multiplying the factors. If the polynomial doesn’t factor,
write “prime.”
16. y2 - 13y + 12 ______________ 17. x2 + 7x – 18 ______________
18. y2 – 7y + 12
______________ 19. j2 – 7j + 10 _______________
20. y2 - 8y + 12
______________ 21. y2 – 11y – 12 _______________
22. r2 + 16r + 28 ______________ 23. y2 - 4y – 12 _______________
24. y2 + 12y + 36 ______________ 25. y2 - y – 12 ________________
26. h2 – 12h + 27 ______________ 27. x2 - 4x + 3 _______________
28. a2 + 4a – 32 ______________ 29. d2+ 8d + 7 _______________
30. w2 + 14w + 33 ______________ 31. d2 – 2d + 1 ________________
32. r2 – 13r + 22 ______________ 33. g2 + 7g + 49 _______________
34. p2 – 12p + 11 ______________ 35. b2 + 6b – 91 _______________
36. f2 – 10f + 16 ______________ 37. b2 + 14b + 45 ______________
38. n2 + 19n + 48 ______________ 39. a2 + 24a + 23 ______________
Ch 8 Handouts Alg 1H
8-A3 Handout
Alg 1H
Factor each expression completely.
1) 6y2 – 23y + 7
2) 3x2 – 2x – 6
3) 14x2 – 19x – 40
4) 2n2 + 9n + 10
5) 2n2 + 5n – 25
6) 5x2 + 25x + 30
7) 6a3 + 42a2 + 72a
8) 8x2 – 2x + 12xy – 3y
9) ax2 – ax – 42a
10) 3x2 + 8x + 5
11) 6x2 + 5x – 4
12) 30a2 – 5a – 5
13) 2x2 – 9x – 35
14) 7a2 + 49a + 84
15) 36y2 + 13y – 40
Ch 8 Handouts Alg 1H
16) ny4 – 8ny2 + 15n
17) 14x2 – 12x3 – 4x
18) 48jx2 + 14jx – 12j
19) 6x3 + 15x2 – 16x – 40
20) 48x3 – 2x2 – 20x
21) 10x3 + 5x2 – 30x
22) 10x3 + 15x2 – 8x – 12
23) 12x3 – 21x2 – 6x
24) 42y4 – 76y3 + 10y2
25) Solve: 5x2 = 5x
26) Solve: (x + 2) (x – 3) = 24
27) The product of two consecutive positive integers is 11 more than their
sum. Write an equation and solve to find the integers.
Ch 8 Handouts Alg 1H
8-A5 Class Work
Algebra 1H
You may write on this handout.
Name__________________________
Extra Practice Factoring and Solving Quadratic Equations
Factor each trinomial, if possible. If the trinomial cannot be factored using integers, write prime.
1) 2b2 + 10b +12
2) 3g2 + 8g + 4
3) 4x2 + 4x – 3
4) 8b2 – 5b – 10
5) 6m2 + 7m – 3
6) 10d2 + 17d – 20
7) 6a2 – 17a + 12
8) 8w2 – 18w + 9
9) 10x2 – 9x + 6
10) 15n2 – n – 28
11) 10x2 + 21x – 10
12) 9r2 + 15r + 6
13) 12y2 – 4y – 5
14) 14k2 – 9k – 18
15) 8z2 + 20z – 48
16) 12q2 + 34q – 28
17) 18h2 + 15h – 18
18) 12p2 – 22p – 20
Solve each equation. Check your solutions.
19) 3h2 + 2h – 16 = 0
21) 8q2 – 10q + 3 = 0
20) 15n2 – n = 2
22) 6b2 – 5b = 4
over →
Ch 8 Handouts Alg 1H
23) 10c2 – 21c = –4c + 6
27) 12k2 + 15k = 16k + 20
24) 10g2 + 10 = 29g
28) 12x2 – 1 = –x
25) 6y2 = –7y – 2
29) 8a2 – 16a = 6a – 12
26) 9z2 = –6z + 15
30) 18a2 + 10a = –11a + 4
Write a quadratic equation, solve it, and give a word answer.
31) The length of a rectangular lawn is 20 yards greater than its width. If the area of
the lawn is 300 square yards, find the dimensions of the lawn.
32) Five less than a number squared is 30 more than twice the number. Find the
number.
Ch 8 Handouts Alg 1H
8-A5 HW PRACTICE FOR QUIZ 8-4
Alg 1H
Factor:
1) x2 + 6x – 16
2) x2 + x – 30
3) 12x2 – 9x + 15
4) 6x2 – 11x – 10
5) 14x2 –15x + 4
6) 6x2 – 21x – 9
7) 3x2 – 37x + 44
8) 2xy – x + 4y – 2
9) 2x2 + 4x – 8
10) 4x2 + 32x + 63
11) 12x2 + 45x + 92
12) 5x2 – 40x – 100
13) 6x2 + x – 70
14) 2x2 + 19x – 10
16) 12x2 + 7x + 1
17) 6xy2 + 33xy – 63x
18) -8x3 + 38x2 + 10x
19) 3x2 + 30x + 72
20) x3 – 7x2 + 12x
21) 10t2 – 15t – 25
15) ab – 2ac + 5b – 10c
Fill in the blanks.
22) The Zero Product Property tells us that if ab = 0, then_____________ will = 0.
23) When you are asked to find the roots of an equation, this is another way of asking
for the ______________ of the equation.
Solve:
24) p2 – 7p – 60 = 0
25) y2 – 4y = 21
27) 2x2 – 7x = 15
28) x3 + 7x2 – 60x = 0
29) 10x2 – 43x + 45 = 0
26) 6x2 = 2x
30) 2(x2 + 5) = 9x
For # 31-32 write and solve an equation to answer the question.
31)
When a positive number is added to its square, the sum is 72. Find the number.
32)
The length and width of a rectangle are consecutive integers. If the area of the
rectangle is 90 cm2, find the dimensions of the rectangle.
Ch 8 Handouts Alg 1H
8-A8
Using Factoring to Solve Quadratic Word Problems
Algebra 1H
Show all work neatly on separate paper. Label your variables, write a quadratic equation, solve, and then
answer the problem. Remember, word problems need word answers.
1.
A positive number is 30 less than its square. Find the number.
2.
Find 2 consecutive positive odd integers whose product is 143.
3.
The sum of the squares of 2 consecutive negative even integers is 100. Find them.
4.
The length of a rectangle is 8 cm greater than its width. Find the dimensions of the rectangle
if its area is 105 cm2.
The length of a rectangle is 6 cm less than twice its width. Find the dimensions of the
rectangle if its area is 108 cm2.
Find the dimensions of a rectangle whose perimeter is 46 cm and whose area is 126 cm2.
5.
6.
(Hint: Let the width be w. Use the perimeter to find the length in terms of w).
7.
Originally the dimensions of a rectangle were 20 cm by 23 cm. When both dimensions were
decreased by the same amount, the area of the rectangle decreased by 120 cm2. Find the
dimensions of the new rectangle.
8.
Originally a rectangle was twice as long as it was wide. When 4 m were added to its length
and 3m subtracted from its width, the resulting rectangle had an area of 600m 2. Find the
dimensions of the new rectangle.
In exercises 9 - 14, use the formula
h   4.9t2  vt  s where h is in meters and the formula
h   16t2  vt  s when h is in feet. (h = height, v = initial velocity, t = time in seconds)
9.
A ball is thrown upward with an initial speed of 24.5 m/s. When is it 19.6 m high? (2 answers)
10. A watermelon is dropped from a bridge that is 208 feet high. How long will it take for the
watermelon to hit the water under the bridge?
11. A park has a vertical motion ride where passengers are launched straight upward from ground
level with an initial velocity of 96 ft/s. How many seconds after launch will the car reach 144
ft.?
12. Mitch tossed an apple up to Kathy, who was on a balcony 40 ft. above him, with an initial speed
of 56 ft/s. Kathy missed the apple on the way up, but caught it on its way down. How long
was the apple in the air?
13. A rocket is fired upward with an initial velocity of 160 ft/s.
a. When is the rocket 400 ft. high?
b. How do you know that 400 ft. is the greatest height the rocket reaches?
14. A rocket is fired upward with an initial speed of 1960 m/s. after how many minutes does it
hit the
ground.
Algebra 1H
Ch 8 Handouts Alg 1H
T2-Rev. Practice Sheet
General Practice for the Trimester 2 Final Exam
There are graphs on this assignment so it will need to be done on graph paper. All word
problems need: let statements, equation (or equations), work shown, and a final word
answer.
1.
Solve:
5x – 2(1  x) = 2(1  2x)
2.
Jason bought bouquets of flowers to sell in his flower shop on Valentine’s Day. He
paid $5 for each bouquet and he sold all but 10 of them for $12 each. His profit was
$1000. How many bouquets of flowers did he buy?
For # 3 – 5 Write the equation or inequality in SLOPE INTERCEPT FORM, then sketch its graph.
3. 4x  5y = 15
6.
4. x  3y = 3x  6
5. 2x + 3y  x – 9
For the absolute value equation y = 2 x  3  5 (a) Find the coordinates of the
vertex. (b) Find the x-intercepts algebraically (show work). (c) Graph
7.
8.
1
and y = 4.
2
xy
3x  4 y
Write the equation of the line that passes through the point (‫ ־‬2, 6) and is
Evaluate the following expression for x =
PARALLEL to the line with the equation 5x + 3y = 15. Put your final answer in SLOPE
INTERCEPT FORM.
9.
Write an equation of the line that passes through (4, ‫ ־‬2) and is PERPENDICULAR to
2
the line with the equation y = x + 1. Put your final answer in SLOPE INTERCEPT FORM.
3
10. Find the equation of the line that passes through the points (0,2) and (4, ‫ ־‬5).
Write your final answer in STANDARD FORM.
11.
A rectangular swimming pool is 6 m longer than it is wide. A cement walk 2 m wide
surrounds it. The area of the walk is 112 m2. Find the dimensions of the pool.
12. Two planes leave Santa Fe New Mexico at the same time, one traveling east and the
other west. The speed of the eastbound plane is 60 km/h more than the speed of the
westbound plane. After 3 hours the planes are 4500 km apart. What is the speed of the
westbound plane?
13. How many milliliters of water must be added to 60 ml of a 15 % iodine solution in
order to dilute it to a 10% solution?
14.
A rectangle has an area of 2x2 + 13x + 15 square meters. Express the perimeter of
the rectangle as a simplified expression.
Ch 8 Handouts Alg 1H