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Mathematics LibreTexts

6.10: Exercise Supplement

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Exercise Supplement

Finding the factors of a Monomial

For the following problems, the first quantity represents the product and the second quantity represents a factor. Find the other factor.

Exercise 6.10.1

32a4b,2b

Answer

16a4

Exercise 6.10.2

35x3y2,7x3

Exercise 6.10.3

44a2b2c,11b2

Answer

4a2c

Exercise 6.10.4

50m3n5p4q,10m3q

Exercise 6.10.5

51(a+1)2(b+3)4,3(a+1)

Answer

17(a+1)(b+3)4

Exercise 6.10.6

26(x+2y)3(xy)2,13(xy)

Exercise 6.10.7

8x5y4(x+y)4(x+3y)3,2x(x+y)(x+3y)

Answer

4x4y4(x+y)3(x+3y)2

Exercise 6.10.8

(6a5b)10(7ab)8(a+3b)7,(6a5b)7(7ab)7(a+3b)7

Exercise 6.10.9

12xn+6y2n5,3xn+1yn+3

Answer

4x5yn8

Exercise 6.10.10

400a3n+10bn6c4n+7,20a2n+8c2n1

Exercise 6.10.11

16x32,16

Answer

(x2)

Exercise 6.10.12

35a45,513

Exercise 6.10.13

24a26a,6a

Answer

4a1

Exercise 6.10.14

88x433x3+44x2+55x,11x

Exercise 6.10.15

9y327y2+36y,3y

Answer

3y2+9y12

Exercise 6.10.16

4m616m4+16m2,4m

Exercise 6.10.17

5x4y3+10x3y215x2y2,5x2y2

Answer

x2y2x+3

Exercise 6.10.18

21a5b6c4(a+2)3+35a5bc5(a+2)4,7a4b(a+2)2

Exercise 6.10.19

x2yc2,1

Answer

x+2y+c2

Exercise 6.10.20

a+3b,1

Factoring a Monomial from a Polynomial ([link]) - The Greatest Common Factor ([link])

For the following problems, factor the polynomials.

Exercise 6.10.21

8a+4

Answer

4(2a+1)

Exercise 6.10.22

10x+10

Exercise 6.10.23

3y2+27y

Answer

3y(y+9)

Exercise 6.10.24

6a2b2+18a2

Exercise 6.10.25

21(x+5)+9

Answer

3(7x+38)

Exercise 6.10.26

14(2a+1)+35

Exercise 6.10.27

ma3m

Answer

m(a31)

Exercise 6.10.28

15y324y+24

Exercise 6.10.29

r2(r+1)33r(r+1)2+r+1

Answer

(r+1)[r2(r+1)23r(r+1)+1]

Exercise 6.10.30

Pa+Pb+Pc

Exercise 6.10.31

(103x)(2+x)+3(103x)(7+x)

Answer

(103x)(23+4x)

Factoring by Grouping

For the following problems, use the grouping method to factor the polynomials. Some may not be factorable.

Exercise 6.10.32

4ax+x+4ay+y

Exercise 6.10.33

xy+4x3y12

Answer

(x3)(y+4)

Exercise 6.10.34

2ab8b3ab12a

Exercise 6.10.35

a27a+ab7b

Answer

(a+b)(a7)

Exercise 6.10.36

m2+5m+nm+5n

Exercise 6.10.37

r2+rsrs

Answer

(r1)(r+s)

Exercise 6.10.38

8a2bc+20a2bc+10a3b3c+25a3b3

Exercise 6.10.39

a(a+6)(a+6)+a(a4)(a4)

Answer

2(a+1)(a1)

Exercise 6.10.40

a(2x+7)4(2x+7)+a(x10)4(x10)

Factoring Two Special Products - Factoring Trinomials with Leading Coefficient Other Than 1

For the following problems, factor the polynomials, if possible.

Exercise 6.10.41

m236

Answer

(m+6)(m6)

Exercise 6.10.42

r281

Exercise 6.10.43

a2+8a+16

Answer

(a+4)2

Exercise 6.10.44

c2+10c+25

Exercise 6.10.45

m2+m+1

Answer

not factorable

Exercise 6.10.46

r2r6

Exercise 6.10.47

a2+9a+20

Answer

(a+5)(a+4)

Exercise 6.10.48

s2+9s+18

Exercise 6.10.49

x2+14x+40

Answer

(x+10)(x+4)

Exercise 6.10.50

a212a+36

Exercise 6.10.51

n214n+49

Answer

(n7)2

Exercise 6.10.52

a2+6a+5

Exercise 6.10.53

a29a+20

Answer

(a5)(a4)

Exercise 6.10.54

6x2+5x+1

Exercise 6.10.55

4a29a9

Answer

(4a+3)(a3)

Exercise 6.10.56

4x2+7x+3

Exercise 6.10.57

42a2+5a2

Answer

(6a1)(7a+2)

Exercise 6.10.58

30y2+7y15

Exercise 6.10.59

56m2+26m+6

Answer

2(28m2+13m+3)

Exercise 6.10.60

27r233r4

Exercise 6.10.61

4x2+4xy3y2

Answer

(2x+3y)(2xy)

Exercise 6.10.62

25a2+25ab+6b2

Exercise 6.10.63

2x2+6x20

Answer

2(x2)(x+5)

Exercise 6.10.64

2y2+4y+48

Exercise 6.10.65

x3+3x24x

Answer

x(x+4)(x1)

Exercise 6.10.66

3y427y3+24y2

Exercise 6.10.67

15a2b2ab2b

Answer

b(15a2ba2)

Exercise 6.10.68

4x316x2+16x

Exercise 6.10.69

18a26a+12

Answer

(6a1)(3a12)

Exercise 6.10.70

a4+16a2b+16b2

Exercise 6.10.71

4x212xy+9y2

Answer

(2x3y)2

Exercise 6.10.72

49b484b2+36

Exercise 6.10.73

r6s8+6r3s4p2q6+9p4q12

Answer

(r3s4+3p2q6)2

Exercise 6.10.74

a42a2b15b2

Exercise 6.10.75

81a8b12c1025x20y18

Answer

(9a4b6c5+5x10y9)(9a4b6c55x10y9)


This page titled 6.10: Exercise Supplement is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Denny Burzynski & Wade Ellis, Jr. (OpenStax CNX) .

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