^{2}+16y+24

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Factors of Algebraic Expressions

Name
Grade
School

Date
Questions20
Score

1

2y^{2}+16y+24

2

x^{2}-17x+42

3

x^{2}-6x+8

4

y^{2}-7y+10

5

x^{2}-5x+6

6

5y^{2}+25y+30

7

z^{2}-9z+14

8

x^{2}-9x+20

9

y^{2}-8y+15

10

y^{2}-10y+16

11

x^{2}-15x+50

12

x^{2}-7x+10

13

2z^{2}+12z+18

14

y^{2}-16y+55

15

x^{2}-11x+30

16

y^{2}-12y+20

17

z^{2}-11z+24

18

x^{2}-4x-21

19

3m^{2}+15m+18

20

x^{2}-4x-12

Solved Worksheet Problems

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1

2y^{2}+16y+24

2 (y+2) (y+6)

2 (y+2) (y+6)

Solution

2y^{2}+16y +24 = 0

2(y^{2}+8y +12) = y^{2}+8y +12

.`. Factors of 12 = 2 x 6 and 2 + 6 = 8

=> y^{2}+2y+6y+12

=> y(y+2) + 6(y+2)

=> 2 (y+2) (y+6)

2(y

.`. Factors of 12 = 2 x 6 and 2 + 6 = 8

=> y

=> y(y+2) + 6(y+2)

=> 2 (y+2) (y+6)

2

x^{2}-17x+42

(x-3) (x-14)

(x-3) (x-14)

Solution

x^{2}-17x +42 = 0

.`. Factors of 42 = 3 x 14 and 3 + 14 = 17

=> x^{2}-3x-14x+42

=> x(x-3) - 14(x-3)

=> (x-3) (x-14)

.`. Factors of 42 = 3 x 14 and 3 + 14 = 17

=> x

=> x(x-3) - 14(x-3)

=> (x-3) (x-14)

3

x^{2}-6x+8

(x-2) (x-4)

(x-2) (x-4)

Solution

x^{2}-6x +8 = 0

.`. Factors of 8 = 2 x 4 and 2 + 4 = 6

=> x^{2}-2x-4x+8

=> x(x-2) - 4(x-2)

=> (x-2) (x-4)

.`. Factors of 8 = 2 x 4 and 2 + 4 = 6

=> x

=> x(x-2) - 4(x-2)

=> (x-2) (x-4)

4

y^{2}-7y+10

(y-2) (y-5)

(y-2) (y-5)

Solution

y^{2}-7y +10 = 0

.`. Factors of 10 = 2 x 5 and 2 + 5 = 7

=> y^{2}-2y-5y+10

=> y(y-2) - 5(y-2)

=> (y-2) (y-5)

.`. Factors of 10 = 2 x 5 and 2 + 5 = 7

=> y

=> y(y-2) - 5(y-2)

=> (y-2) (y-5)

5

x^{2}-5x+6

(x-2) (x-3)

(x-2) (x-3)

Solution

x^{2}-5x +6 = 0

.`. Factors of 6 = 2 x 3 and 2 + 3 = 5

=> x^{2}-2x-3x+6

=> x(x-2) - 3(x-2)

=> (x-2) (x-3)

.`. Factors of 6 = 2 x 3 and 2 + 3 = 5

=> x

=> x(x-2) - 3(x-2)

=> (x-2) (x-3)

6

5y^{2}+25y+30

5 (y+2) (y+3)

5 (y+2) (y+3)

Solution

5y^{2}+25y +30 = 0

5(y^{2}+5y +6) = y^{2}+5y +6

.`. Factors of 6 = 2 x 3 and 2 + 3 = 5

=> y^{2}+2y+3y+6

=> y(y+2) + 3(y+2)

=> 5 (y+2) (y+3)

5(y

.`. Factors of 6 = 2 x 3 and 2 + 3 = 5

=> y

=> y(y+2) + 3(y+2)

=> 5 (y+2) (y+3)

7

z^{2}-9z+14

(z-2) (z-7)

(z-2) (z-7)

Solution

z^{2}-9z +14 = 0

.`. Factors of 14 = 2 x 7 and 2 + 7 = 9

=> z^{2}-2z-7z+14

=> z(z-2) - 7(z-2)

=> (z-2) (z-7)

.`. Factors of 14 = 2 x 7 and 2 + 7 = 9

=> z

=> z(z-2) - 7(z-2)

=> (z-2) (z-7)

8

x^{2}-9x+20

(x-4) (x-5)

(x-4) (x-5)

Solution

x^{2}-9x +20 = 0

.`. Factors of 20 = 4 x 5 and 4 + 5 = 9

=> x^{2}-4x-5x+20

=> x(x-4) - 5(x-4)

=> (x-4) (x-5)

.`. Factors of 20 = 4 x 5 and 4 + 5 = 9

=> x

=> x(x-4) - 5(x-4)

=> (x-4) (x-5)

9

y^{2}-8y+15

(y-3) (y-5)

(y-3) (y-5)

Solution

y^{2}-8y +15 = 0

.`. Factors of 15 = 3 x 5 and 3 + 5 = 8

=> y^{2}-3y-5y+15

=> y(y-3) - 5(y-3)

=> (y-3) (y-5)

.`. Factors of 15 = 3 x 5 and 3 + 5 = 8

=> y

=> y(y-3) - 5(y-3)

=> (y-3) (y-5)

10

y^{2}-10y+16

(y-2) (y-8)

(y-2) (y-8)

Solution

y^{2}-10y +16 = 0

.`. Factors of 16 = 2 x 8 and 2 + 8 = 10

=> y^{2}-2y-8y+16

=> y(y-2) - 8(y-2)

=> (y-2) (y-8)

.`. Factors of 16 = 2 x 8 and 2 + 8 = 10

=> y

=> y(y-2) - 8(y-2)

=> (y-2) (y-8)

11

x^{2}-15x+50

(x-5) (x-10)

(x-5) (x-10)

Solution

x^{2}-15x +50 = 0

.`. Factors of 50 = 5 x 10 and 5 + 10 = 15

=> x^{2}-5x-10x+50

=> x(x-5) - 10(x-5)

=> (x-5) (x-10)

.`. Factors of 50 = 5 x 10 and 5 + 10 = 15

=> x

=> x(x-5) - 10(x-5)

=> (x-5) (x-10)

12

x^{2}-7x+10

(x-2) (x-5)

(x-2) (x-5)

Solution

x^{2}-7x +10 = 0

.`. Factors of 10 = 2 x 5 and 2 + 5 = 7

=> x^{2}-2x-5x+10

=> x(x-2) - 5(x-2)

=> (x-2) (x-5)

.`. Factors of 10 = 2 x 5 and 2 + 5 = 7

=> x

=> x(x-2) - 5(x-2)

=> (x-2) (x-5)

13

2z^{2}+12z+18

2 (z+3) (z+3)

2 (z+3) (z+3)

Solution

2z^{2}+12z +18 = 0

2(z^{2}+6z +9) = z^{2}+6z +9

.`. Factors of 9 = 3 x 3 and 3 + 3 = 6

=> z^{2}+3z+3z+9

=> z(z+3) + 3(z+3)

=> 2 (z+3) (z+3)

2(z

.`. Factors of 9 = 3 x 3 and 3 + 3 = 6

=> z

=> z(z+3) + 3(z+3)

=> 2 (z+3) (z+3)

14

y^{2}-16y+55

(y-5) (y-11)

(y-5) (y-11)

Solution

y^{2}-16y +55 = 0

.`. Factors of 55 = 5 x 11 and 5 + 11 = 16

=> y^{2}-5y-11y+55

=> y(y-5) - 11(y-5)

=> (y-5) (y-11)

.`. Factors of 55 = 5 x 11 and 5 + 11 = 16

=> y

=> y(y-5) - 11(y-5)

=> (y-5) (y-11)

15

x^{2}-11x+30

(x-5) (x-6)

(x-5) (x-6)

Solution

x^{2}-11x +30 = 0

.`. Factors of 30 = 5 x 6 and 5 + 6 = 11

=> x^{2}-5x-6x+30

=> x(x-5) - 6(x-5)

=> (x-5) (x-6)

.`. Factors of 30 = 5 x 6 and 5 + 6 = 11

=> x

=> x(x-5) - 6(x-5)

=> (x-5) (x-6)

16

y^{2}-12y+20

(y-2) (y-10)

(y-2) (y-10)

Solution

y^{2}-12y +20 = 0

.`. Factors of 20 = 2 x 10 and 2 + 10 = 12

=> y^{2}-2y-10y+20

=> y(y-2) - 10(y-2)

=> (y-2) (y-10)

.`. Factors of 20 = 2 x 10 and 2 + 10 = 12

=> y

=> y(y-2) - 10(y-2)

=> (y-2) (y-10)

17

z^{2}-11z+24

(z-3) (z-8)

(z-3) (z-8)

Solution

z^{2}-11z +24 = 0

.`. Factors of 24 = 3 x 8 and 3 + 8 = 11

=> z^{2}-3z-8z+24

=> z(z-3) - 8(z-3)

=> (z-3) (z-8)

.`. Factors of 24 = 3 x 8 and 3 + 8 = 11

=> z

=> z(z-3) - 8(z-3)

=> (z-3) (z-8)

18

x^{2}-4x-21

(x+3) (x-7)

(x+3) (x-7)

Solution

x^{2}-4x -21 = 0

.`. Factors of -21 = 3 x -7 and -7 + 3 = -4

=> x^{2}+3x-7x-21

=> x(x+3) - 7(x+3)

=> (x+3) (x-7)

.`. Factors of -21 = 3 x -7 and -7 + 3 = -4

=> x

=> x(x+3) - 7(x+3)

=> (x+3) (x-7)

19

3m^{2}+15m+18

3 (m+2) (m+3)

3 (m+2) (m+3)

Solution

3m^{2}+15m +18 = 0

3(m^{2}+5m +6) = m^{2}+5m +6

.`. Factors of 6 = 2 x 3 and 2 + 3 = 5

=> m^{2}+2m+3m+6

=> m(m+2) + 3(m+2)

=> 3 (m+2) (m+3)

3(m

.`. Factors of 6 = 2 x 3 and 2 + 3 = 5

=> m

=> m(m+2) + 3(m+2)

=> 3 (m+2) (m+3)

20

x^{2}-4x-12

(x+2) (x-6)

(x+2) (x-6)

Solution

x^{2}-4x -12 = 0

.`. Factors of -12 = 2 x -6 and -6 + 2 = -4

=> x^{2}+2x-6x-12

=> x(x+2) - 6(x+2)

=> (x+2) (x-6)

.`. Factors of -12 = 2 x -6 and -6 + 2 = -4

=> x

=> x(x+2) - 6(x+2)

=> (x+2) (x-6)

Online Test

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