<< Chapter < Page Chapter >> Page >

Watermelon drop A watermelon is dropped from the tenth story of a building. Solve the equation −16 t 2 + 144 = 0 for t to find the number of seconds it takes the watermelon to reach the ground.

Got questions? Get instant answers now!

Writing exercises

Explain how you solve a quadratic equation. How many answers do you expect to get for a quadratic equation?

Answers may vary.

Got questions? Get instant answers now!

Give an example of a quadratic equation that has a GCF and none of the solutions to the equation is zero.

Got questions? Get instant answers now!

Self check

After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.

This table has the following statements all to be preceded by “I can…”. The first row is “solve quadratic equations by using the zero product property”. The second row is “solve quadratic equations by factoring”. The third row is “solve applications modeled by quadratic equations”. In the columns beside these statements are the headers, “confidently”, “with some help”, and “no-I don’t get it!”.

Overall, after looking at the checklist, do you think you are well-prepared for the next section? Why or why not?

7.1 Greatest Common Factor and Factor by Grouping

Find the Greatest Common Factor of Two or More Expressions

In the following exercises, find the greatest common factor.

Factor the Greatest Common Factor from a Polynomial

In the following exercises, factor the greatest common factor from each polynomial.

24 x 42

6 ( 4 x 7 )

Got questions? Get instant answers now!

15 m 4 + 6 m 2 n

3 m 2 ( 5 m 2 + 2 n )

Got questions? Get instant answers now!

Factor by Grouping

In the following exercises, factor by grouping.

a x a y + b x b y

( a + b ) ( x y )

Got questions? Get instant answers now!

x 2 y x y 2 + 2 x 2 y

Got questions? Get instant answers now!

x 2 + 7 x 3 x 21

( x 3 ) ( x + 7 )

Got questions? Get instant answers now!

4 x 2 16 x + 3 x 12

Got questions? Get instant answers now!

m 3 + m 2 + m + 1

( m 2 + 1 ) ( m + 1 )

Got questions? Get instant answers now!

7.2 Factor Trinomials of the form x 2 + b x + c

Factor Trinomials of the Form x 2 + b x + c

In the following exercises, factor each trinomial of the form x 2 + b x + c .

u 2 + 17 u + 72

( u + 8 ) ( u + 9 )

Got questions? Get instant answers now!

k 2 16 k + 60

( k 6 ) ( k 10 )

Got questions? Get instant answers now!

y 2 + 6 y 7

( y + 7 ) ( y 1 )

Got questions? Get instant answers now!

s 2 2 s 8

( s 4 ) ( s + 2 )

Got questions? Get instant answers now!

Factor Trinomials of the Form x 2 + b x y + c y 2

In the following examples, factor each trinomial of the form x 2 + b x y + c y 2 .

x 2 + 12 x y + 35 y 2

( x + 5 y ) ( x + 7 y )

Got questions? Get instant answers now!

a 2 + 4 a b 21 b 2

( a + 7 b ) ( a 3 b )

Got questions? Get instant answers now!

p 2 5 p q 36 q 2

Got questions? Get instant answers now!

7.3 Factoring Trinomials of the form a x 2 + b x + c

Recognize a Preliminary Strategy to Factor Polynomials Completely

In the following exercises, identify the best method to use to factor each polynomial.

y 2 17 y + 42

Undo FOIL

Got questions? Get instant answers now!

8 a 3 + 72 a

Factor the GCF

Got questions? Get instant answers now!

4 m m n 3 n + 12

Got questions? Get instant answers now!

Factor Trinomials of the Form a x 2 + b x + c with a GCF

In the following exercises, factor completely.

6 x 2 + 42 x + 60

6 ( x + 2 ) ( x + 5 )

Got questions? Get instant answers now!

3 n 4 12 n 3 96 n 2

3 n 2 ( n 8 ) ( n + 4 )

Got questions? Get instant answers now!

Factor Trinomials Using the “ac” Method

In the following exercises, factor.

2 x 2 + 9 x + 4

( x + 4 ) ( 2 x + 1 )

Got questions? Get instant answers now!

18 a 2 9 a + 1

( 3 a 1 ) ( 6 a 1 )

Got questions? Get instant answers now!

15 p 2 + 2 p 8

( 5 p + 4 ) ( 3 p 2 )

Got questions? Get instant answers now!

40 s 2 s 6

( 5 s 2 ) ( 8 s + 3 )

Got questions? Get instant answers now!

Factor Trinomials with a GCF Using the “ac” Method

In the following exercises, factor.

3 x 2 + 3 x 36

3 ( x + 4 ) ( x 3 )

Got questions? Get instant answers now!

60 y 2 85 y 25

5 ( 4 y + 1 ) ( 3 y 5 )

Got questions? Get instant answers now!

7.4 Factoring Special Products

Factor Perfect Square Trinomials

In the following exercises, factor.

25 x 2 + 30 x + 9

( 5 x + 3 ) 2

Got questions? Get instant answers now!

36 a 2 84 a b + 49 b 2

( 6 a 7 b ) 2

Got questions? Get instant answers now!

64 r 2 176 r s + 121 s 2

Got questions? Get instant answers now!

40 x 2 + 360 x + 810

10 ( 2 x + 9 ) 2

Got questions? Get instant answers now!

2 y 3 16 y 2 + 32 y

2 y ( y 4 ) 2

Got questions? Get instant answers now!

5 k 3 70 k 2 + 245 k

Got questions? Get instant answers now!

Factor Differences of Squares

In the following exercises, factor.

81 r 2 25

( 9 r 5 ) ( 9 r + 5 )

Got questions? Get instant answers now!

169 m 2 n 2

( 13 m + n ) ( 13 m n )

Got questions? Get instant answers now!

25 p 2 1

( 5 p 1 ) ( 5 p + 1 )

Got questions? Get instant answers now!

9 121 y 2

( 3 + 11 y ) ( 3 11 y )

Got questions? Get instant answers now!

20 x 2 125

5 ( 2 x 5 ) ( 2 x + 5 )

Got questions? Get instant answers now!

49 u 3 9 u

u ( 7 u + 3 ) ( 7 u 3 )

Got questions? Get instant answers now!

Factor Sums and Differences of Cubes

In the following exercises, factor.

a 3 125

( a 5 ) ( a 2 + 5 a + 25 )

Got questions? Get instant answers now!

2 m 3 + 54

2 ( m + 3 ) ( m 2 3 m + 9 )

Got questions? Get instant answers now!

7.5 General Strategy for Factoring Polynomials

Recognize and Use the Appropriate Method to Factor a Polynomial Completely

In the following exercises, factor completely.

24 x 3 + 44 x 2

4 x 2 ( 6 x + 11 )

Got questions? Get instant answers now!

16 n 2 56 m n + 49 m 2

( 4 n 7 m ) 2

Got questions? Get instant answers now!

5 r 2 + 22 r 48

( r + 6 ) ( 5 r 8 )

Got questions? Get instant answers now!

n 4 81

( n 2 + 9 ) ( n + 3 ) ( n 3 )

Got questions? Get instant answers now!

5 x 2 + 5 x 60

5 ( x 3 ) ( x + 4 )

Got questions? Get instant answers now!

m 3 + 125

( m + 5 ) ( m 2 5 m + 25 )

Got questions? Get instant answers now!

2 b 2 2 b c + 5 c b 5 c 2

Got questions? Get instant answers now!

7.6 Quadratic Equations

Use the Zero Product Property

In the following exercises, solve.

( a 3 ) ( a + 7 ) = 0

a = 3 a = −7

Got questions? Get instant answers now!

( b 3 ) ( b + 10 ) = 0

Got questions? Get instant answers now!

3 m ( 2 m 5 ) ( m + 6 ) = 0

m = 0 m = −3 m = 5 2

Got questions? Get instant answers now!

7 n ( 3 n + 8 ) ( n 5 ) = 0

Got questions? Get instant answers now!

Solve Quadratic Equations by Factoring

In the following exercises, solve.

x 2 + 9 x + 20 = 0

x = −4 , x = −5

Got questions? Get instant answers now!

2 p 2 11 p = 40

p = 5 2 , p = 8

Got questions? Get instant answers now!

144 m 2 25 = 0

m = 5 12 , m = 5 12

Got questions? Get instant answers now!

Solve Applications Modeled by Quadratic Equations

In the following exercises, solve.

The product of two consecutive numbers is 462 . Find the numbers.

−21 , −22 21 , 22

Got questions? Get instant answers now!

The area of a rectangular shaped patio 400 square feet. The length of the patio is 9 feet more than its width. Find the length and width.

Got questions? Get instant answers now!

Practice test

In the following exercises, find the Greatest Common Factor in each expression.

14 y 42

7 ( y 6 )

Got questions? Get instant answers now!

80 a 2 + 120 a 3

40 a 2 ( 2 + 3 a )

Got questions? Get instant answers now!

5 m ( m 1 ) + 3 ( m 1 )

Got questions? Get instant answers now!

In the following exercises, factor completely.

x 2 + 13 x + 36

( x + 7 ) ( x + 6 )

Got questions? Get instant answers now!

3 a 3 6 a 2 72 a

3 a ( a 2 2 a 14 )

Got questions? Get instant answers now!

5 n 2 + 30 n + 45

5 ( n + 1 ) ( n + 5 )

Got questions? Get instant answers now!

x y 8 y + 7 x 56

( x 8 ) ( y + 7 )

Got questions? Get instant answers now!

9 s 2 12 s + 4

( 3 s 2 ) 2

Got questions? Get instant answers now!

100 a 2

( 10 a ) ( 10 + a )

Got questions? Get instant answers now!

3 x 2 75 y 2

3 ( x + 5 y ) ( x 5 y )

Got questions? Get instant answers now!

a b 3 b 2 a + 6

( a 3 ) ( b 2 )

Got questions? Get instant answers now!

8 m 2 + 22 m + 5

( 4 m + 1 ) ( 2 m + 5 )

Got questions? Get instant answers now!

In the following exercises, solve.

y 2 = y + 132

y = −11 , y = 12

Got questions? Get instant answers now!

9 b 2 9 = 0

b = 1 , b = −1

Got questions? Get instant answers now!

4 n 2 + 19 + 21 = 0

n = 7 4 , n = −3

Got questions? Get instant answers now!

( x 3 ) ( x + 2 ) = 6

Got questions? Get instant answers now!

The product of two consecutive integers is 156 . Find the integers.

12 and 13 ; 13 and −12

Got questions? Get instant answers now!

The area of a rectangular place mat is 168 square inches. Its length is two inches longer than the width. Find the length and width of the placemat.

Got questions? Get instant answers now!

Questions & Answers

Larry and Tom were standing next to each other in the backyard when Tom challenged Larry to guess how tall he was. Larry knew his own height is 6.5 feet and when they measured their shadows, Larry’s shadow was 8 feet and Tom’s was 7.75 feet long. What is Tom’s height?
genevieve Reply
6.25
Ciid
Wayne is hanging a string of lights 57 feet long around the three sides of his patio, which is adjacent to his house. the length of his patio, the side along the house, is 5 feet longer than twice it's width. Find the length and width of the patio.
Katherine Reply
complexed. could you please help me figure out?
Ciid
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
(sin=opp/adj) (tan= opp/adj) cos=hyp/adj dont quote me on it look it up
tyler
SOH = Sine is Opposite over Hypotenuse. CAH= Cosine is Adjacent over Hypotenuse. TOA = Tangent is Opposite over Adjacent.
tyler
H=57 and O=285 figure out what the adjacent?
tyler
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal?
Marisol Reply
what is the quantity and price of the televisions for both options?
karl
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000 17000+
Ciid
Amara has to sell 120 televisions to make 29,000 of the salary of company B. 120 * TV 100= commission 12,000+ 17,000 = of company a salary 29,000
Ciid
I'm mathematics teacher from highly recognized university.
Mzo Reply
here a question professor How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths as many sailors as soldiers? can you write out the college you went to with the name of the school you teach at and let me know the answer I've got it to be honest with you
tyler
is anyone else having issues with the links not doing anything?
Helpful Reply
Yes
Val
chapter 1 foundations 1.2 exercises variables and algebraic symbols
theresa Reply
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold? Enter the answers in decimal form.
Samer Reply
Joseph would like to make 12 pounds of a coffee blend at a cost of $6.25 per pound. He blends Ground Chicory at $4.40 a pound with Jamaican Blue Mountain at $8.84 per pound. How much of each type of coffee should he use?
Samer
4x6.25= $25 coffee blend 4×4.40= $17.60 ground chicory 4x8.84= 35.36 blue mountain. In total they will spend for 12 pounds $77.96 they will spend in total
tyler
DaMarcus and Fabian live 23 miles apart and play soccer at a park between their homes. DaMarcus rode his bike for three-quarters of an hour and Fabian rode his bike for half an hour to get to the park. Fabian’s speed was six miles per hour faster than DaMarcus’ speed. Find the speed of both soccer players.
Sage Reply
i need help how to do this is confusing
Alvina Reply
what kind of math is it?
Danteii
help me to understand
Alvina Reply
huh, what is the algebra problem
Daniel
How many soldiers are there in a group of 27 sailors and soldiers if there are four fifths many sailors as soldiers?
tyler
What is the domain and range of heaviside
Christopher Reply
What is the domain and range of Heaviside and signum
Christopher
25-35
Fazal
The hypotenuse of a right triangle is 10cm long. One of the triangle’s legs is three times the length of the other leg. Find the lengths of the three sides of the triangle.
Edi Reply
Tickets for a show are $70 for adults and $50 for children. For one evening performance, a total of 300 tickets were sold and the receipts totaled $17,200. How many adult tickets and how many child tickets were sold?
Mum Reply
A 50% antifreeze solution is to be mixed with a 90% antifreeze solution to get 200 liters of a 80% solution. How many liters of the 50% solution and how many liters of the 90% solution will be used?
Edi Reply
June needs 45 gallons of punch for a party and has 2 different coolers to carry it in. The bigger cooler is 5 times as large as the smaller cooler. How many gallons can each cooler hold?
Jesus Reply
Practice Key Terms 2

Get the best Elementary algebra course in your pocket!





Source:  OpenStax, Elementary algebra. OpenStax CNX. Jan 18, 2017 Download for free at http://cnx.org/content/col12116/1.2
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Elementary algebra' conversation and receive update notifications?

Ask