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7.2E: Exercises

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Practice Makes Perfect

Factor Trinomials of the Form x2+bx+c

In the following exercises, factor each trinomial of the form x2+bx+c

Exercise 1

x2+4x+3

Answer

(x+1)(x+3)

Exercise 2

y2+8y+7

Exercise 3

m2+12m+11

Answer

(m+1)(m+11)

Exercise 4

b2+14b+13

Exercise 5

a2+9a+20

Answer

(a+4)(a+5)

Exercise 6

m2+7m+12 ​​​​​

Exercise 7

p2+11p+30

Answer

(p+5)(p+6)

Exercise 8

w2+10w+21

Exercise 9

n2+19n+48

Answer

(n+3)(n+16)

Exercise 10

b2+14b+48

Exercise 11

a2+25a+100

Answer

(a+5)(a+20)

Exercise 12

u2+101u+100

Exercise 13

x28x+12

Answer

(x2)(x6)

Exercise 14

q213q+36

Exercise 15

y218y+45

Answer

(y3)(y15)

Exercise 16

m213m+30

Exercise 17

x28x+7

Answer

(x1)(x7)

Exercise 18

y25y+6

Exercise 19

p2+5p6

Answer

(p1)(p+6)

Exercise 20

n2+6n7

Exercise 21

y26y7

Answer

(y+1)(y7)

Exercise 22

v22v3

Exercise 23

x2x12

Answer

(x4)(x+3)

Exercise 24

r22r8

Exercise 25

a23a28

Answer

(a7)(a+4)

Exercise 26

b213b30

Exercise 27

w25w36

Answer

(w9)(w+4)

Exercise 28

t23t54

Exercise 29

x2+x+5

Answer

prime

Exercise 30

x23x9

Exercise 31

86x+x2

Answer

(x4)(x2)

Exercise 32

7x+x2+6

Exercise 33

x21211x

Answer

(x12)(x+1)

Exercise 34

1110x+x2

​​​​​​Factor Trinomials of the Form x2+bxy+cy2

In the following exercises, factor each trinomial of the form x2+bxy+cy2

Exercise 33.2

p2+3pq+2q2

Answer

(p+q)(p+2q)

Exercise 34.2

m2+6mn+5n2

Exercise 35

r2+15rs+36s2

Answer

(r+3s)(r+12s)

Exercise 36

u2+10uv+24v2

Exercise 37

m212mn+20n2

Answer

(m2n)(m10n)

Exercise 38

p216pq+63q2

Exercise 39

x22xy80y2

Answer

(x+8y)(x10y)

Exercise 40

p28pq65q2

Exercise 41

m264mn65n2

Answer

(m+n)(m65n)

Exercise 42

p22pq35q2

Exercise 43

a2+5ab24b2

Answer

(a+8b)(a3b)

Exercise 44

r2+3rs28s2

Exercise 45

x23xy14y2

Answer

prime

Exercise 46

u28uv24v2

Exercise 47

m25mn+30n2

Answer

prime

Exercise 48

c27cd+18d2

​​​​​​Mixed Practice

In the following exercises, factor each expression.

Exercise 49

u212u+36

Answer

(u6)(u6)

Exercise 50

w2+4w32

Exercise 51

x214x32

Answer

(x+2)(x16)

Exercise 52

y2+41y+40

Exercise 53

r220rs+64s2

Answer

(r4s)(r16s)

Exercise 54

x216xy+64y2

Exercise 55

k2+34k+120

Answer

(k+4)(k+30)

Exercise 56

m2+29m+120

Exercise 57

y2+10y+15

Answer

prime

Exercise 58

z23z+28

Exercise 59

m2+mn56n2

Answer

(m+8n)(m7n)

Exercise 60

q229qr96r2

Exercise 61

u217uv+30v2

Answer

(u15v)(u2v)

Exercise 62

m231mn+30n2

Exercise 63

c28cd+26d2

Answer

prime

Exercise 64

r2+11rs+36s2

Everyday Math

Exercise 65

Consecutive integers Deirdre is thinking of two consecutive integers whose product is 56. The trinomial x2+x56 describes how these numbers are related. Factor the trinomial.

Answer

(x+8)(x7)

Exercise 66

Consecutive integers Deshawn is thinking of two consecutive integers whose product is 182. The trinomial x2+x182 describes how these numbers are related. Factor the trinomial describes how these numbers are related. Factor the trinomial.

​​​​​​Writing Exercises

Exercise 67

Many trinomials of the form x2+bx+c factor into the product of two binomials (x+m)(x+n). Explain how you find the values of m and n.

Answer

Answers may vary

Exercise 68

How do you determine whether to use plus or minus signs in the binomial factors of a trinomial of the form x2+bx+c where b and c may be positive or negative numbers?

Exercise 69

Will factored x2x20 as (x+5)(x4). Bill factored it as (x+4)(x5). Phil factored it as (x5)(x4). Who is correct? Explain why the other two are wrong.

Answer

Answers may vary

Exercise 70

Look at Example, where we factored y2+17y+60. We made a table listing all pairs of factors of 60 and their sums. Do you find this kind of table helpful? Why or why not?

​​​​​Self Check

a. 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 is “factor trinomials of the form x ^ 2 +b x + c”. The second is “factor trinomials of the form x^2 + b x y + c y ^ 2”. In the columns beside these statements are the headers, “confidently”, “with some help”, and “no-I don’t get it!”.

b. After reviewing this checklist, what will you do to become confident for all goals?


This page titled 7.2E: Exercises is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.

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