Quiz about GCF and Grouping Test

Question 1

Factor by grouping
x³ - 4x² -4x + 16

Accepted Answer

(x-4)(x² -4)

Answer

(x+4)(x+2)

Answer

(x+4)(x² -4)

Answer

(x-4)(x-2)

Question 2

Factor the Polynomial

2x³+ 5x² + 6x + 15

Accepted Answer

(x² + 3) (2x + 5)

Answer

(x² - 3) (2x - 5)

Answer

(2x² - 3) (x - 5)

Answer

(2x² + 3) (x + 5)

Question 3

Factor the Polynomial

12x³- 9x² + 4x - 3

Accepted Answer

(3x² + 1) (4x - 3)

Answer

(3x² - 1) (4x + 3)

Answer

(4x² + 1) (3x - 3)

Answer

(4x² - 1) (3x + 3)

Question 4

Factor the Polynomial

3x³- 4x² + 9x - 12

Accepted Answer

(x² + 3) (3x - 4)

Answer

(x² - 3) (3x + 4)

Answer

(3x² + 3) (x - 4)

Answer

(3x² - 3) (x + 4)

Question 5

Factor the Polynomial

12x³+ 4x² + 3x + 1

Accepted Answer

(4x² + 1) (3x + 1)

Answer

(4x² - 1) (3x - 1)

Answer

(3x² + 1) (4x + 1)

Answer

(3x² - 1) (4x - 1)

Question 6

Factor the Polynomial

x³- x² + 2x - 2

Accepted Answer

(x² + 2) (x - 1)

Answer

(x² - 2) (x + 1)

Answer

(x² + 1) (x - 2)

Answer

(x² - 1) (x + 2)

Question 7

Factor the Polynomial

5x³- 10x² + 3x - 6

Accepted Answer

(5x² + 3) (x - 2)

Answer

(5x² - 3) (x + 2)

Answer

(x² + 3) (5x - 2)

Answer

(x² - 3) (5x + 2)

Question 8

Factor the Polynomial

8x³- 64x² + x - 8

Accepted Answer

(8x² + 1) (x - 8)

Answer

(8x² - 1) (x + 8)

Answer

(x² + 1) (8x - 8)

Answer

(x² - 1) (8x + 8)

Question 9

Factor the Polynomial

12x³- 21x² + 28x - 49

Accepted Answer

(3x² + 7) (4x - 7)

Answer

(3x² - 7) (4x + 7)

Answer

(4x² + 7) (3x - 7)

Answer

(4x² - 7) (3x + 7)

Question 10

Factor the Polynomial

12x³+ 2x² - 30x - 5

Accepted Answer

(2x² - 5) (6x + 1)

Answer

(2x² + 5) (6x - 1)

Answer

(6x² - 5) (2x + 1)

Answer

(6x² + 5) (2x - 1)

Question 11

Factor the Polynomial

12x³+ 2x² - 30x - 5

Accepted Answer

(2x² - 5) (6x + 1)

Answer

(2x² + 5) (6x - 1)

Answer

(6x² - 5) (2x + 1)

Answer

(6x² + 5) (2x - 1)

Question 12

Factor the Polynomial

6x³- 16x² + 21x - 56

Accepted Answer

(2x² + 7) (3x - 8)

Answer

(2x² - 7) (3x + 8)

Answer

(3x² + 7) (2x - 8)

Answer

(3x² - 7) (2x + 8)

Question 13

Factor the Polynomial

63x³+ 54x² - 105x - 90

Accepted Answer

3(3x² - 5) (7x + 6)

Answer

3(3x² + 5) (7x - 6)

Answer

5(3x² - 5) (7x + 6)

Answer

5(3x² + 5) (7x - 6)

Question 14

Factor the Polynomial

96x³- 84x² + 112x - 98

Accepted Answer

2(6x² + 7) (8x - 7)

Answer

2(6x² - 7) (8x + 7)

Answer

4(6x² + 7) (8x - 7)

Answer

4(6x² - 7) (8x + 7)

Question 15

Factor 4y³+ y + 12y²+ 3 by grouping. Remember to look for common factors first.

Accepted Answer

(4y² + 1)(y + 3)

Answer

4y²(y + 3) + 3

Answer

4y³+ 12y²+ y + 3

Question 16

Factor 28x²+ 63x + 12x + 27 by grouping. Remember to look for common factors first.

Accepted Answer

(7x + 3)(4x + 9)

Answer

(4x + 3)(7x + 9)

Answer

(3x + 7)(4x + 9)

Answer

(9x + 4)(3x + 7)

Question 17

Factor 2x⁹ + 8x⁸+ 3x⁴+ 12x³ by grouping. Remember to look for common factors first.

Accepted Answer

(x³)(2x⁵ + 3)(x + 4)

Answer

(2x⁸ + 3x³)(x + 4)

Answer

(2x⁵ + 3)(x⁴ + 4x³)

Question 18

Factor p³- 3p² - 16p + 48

Accepted Answer

(p + 4) (p - 4) (p - 3)

Answer

p² ( p - 3) (p - 3)

Answer

(p² - 16) (p - 3)

Question 19

Decide if (x-3) is a factor of 3x³+10x²-x-12

Accepted Answer

No, it is not a factor

Answer

Yes, it is a factor

Question 20

Factor by grouping
x³ - 4x² -4x + 16

Accepted Answer

(x-4)(x² -4)

Answer

(x+4)(x+2)

Answer

(x+4)(x² -4)

Answer

(x-4)(x-2)

Question 21

30x³+15x²-18x-9

Accepted Answer

3(5x²-3)(2x+1)

Answer

(5x²-3)(6x+1)

Answer

(5x²-3)(6x+3)

Answer

3(5x²+3)(2x-1)

Question 22

x³-5x²+5x-25

Accepted Answer

(x²+5)(x-5)

Answer

(x²-5)(x-5)

Answer

(x²+5)(x+5)

Answer

(x²-1)(x-25)

Question 23

20x³-25x²+4x-5

Accepted Answer

(5x²+1)(4x-5)

Answer

(5x²-5)(4x+1)

Answer

5(x²-1)(4x+5)

Answer

(5x²+1)(4x-1)

Question 24

7r³-8r²+42r-48

Accepted Answer

(r²+6)(7r-8)

Answer

(r²+6)(7r+8)

Answer

(r²+6)(r²+8)

Answer

(r²+6)(7r+6)

Question 25

7r³-8r²+42r-48

Accepted Answer

(r²+6)(7r-8)

Answer

(r²+6)(7r+8)

Answer

(r²+6)(r²+8)

Answer

(r²+6)(7r+6)

Question 26

Factor by grouping:
3x³-x²+6x-2

Accepted Answer

(x²+2)(3x-1)

Answer

(x²+2)(3x+1)

Answer

(3x³+6x)(x²-2)

Answer

none of the aboe

Question 27

Factor by grouping:

20x³-25x²+4x-5

Accepted Answer

(5x²+1)(4x-5)

Answer

(5x²-5)(4x+1)

Answer

5(x²-1)(4x+5)

Answer

(5x²+1)(4x-1)

Question 28

Factor by grouping:

x³ - 4x² - 4x + 16

Accepted Answer

(x-4)(x² -4)

Answer

(x+4)(x+2)

Answer

(x+4)(x² -4)

Answer

(x-4)(x-2)

Question 29

x³-5x²+5x-25 hint: Factor by Grouping

Accepted Answer

(x²+5)(x-5)

Answer

(x²-5)(x-5)

Answer

(x²+5)(x+5)

Answer

(x²-1)(x-25)

Question 30

30x³+15x²-18x-9 hint: GCF then Factor by Grouping

Accepted Answer

3(5x²-3)(2x+1)

Answer

(5x²-3)(6x+1)

Answer

(5x²-3)(6x+3)

Answer

3(5x²+3)(2x-1)

Question 31

What is the greatest common factor of the two terms in the expression x⁵y²+x²y⁷z

Accepted Answer

x2y2

Answer

x2

Answer

x2y2z

Answer

x5y7z

Question 32

Factor
18a²b⁴c + 24ab³c²

Accepted Answer

6ab³c(3ab + 4c)

Answer

3abc(6ab³+ 8b²c)

Answer

6abc(3ab³ + 4c)

Answer

6ab3c(3b + 4c)

Question 33

Factor
5ab²c¹¹ + 2bc⁵

Accepted Answer

bc⁵(5abc⁶ + 2)

Answer

bc⁵(5ab²c⁶ + 2b)

Answer

b²c⁵(5bc⁶ + 2)

Answer

c4(5a²b²c⁷+ 2bc)

Question 34

Factor
-10xy⁹z + 8y³z⁵

Accepted Answer

2y³z(-5xy⁶ +4z⁴)

Answer

2y⁴z(-20xy⁶ + 4z⁴)

Answer

2y³z(-5xy⁶z + 4z⁵)

Answer

2y³z(-5xy⁶z + 8z⁴)

Question 35

Factor
20p²q² - 25pm

Accepted Answer

5p(4pq² - 5m)

Answer

pm(4q - 5m)

Answer

5(4pq³ - 5m)

Answer

pq(20pq² - 25m)

Question 36

Factor
12j²k³ - 20hj

Accepted Answer

4j(3jk³ - 5h)

Answer

4j(6jk³ - 10h)

Answer

4j(3jk² - 5h)

Answer

4j²(24j²k³ - 20h)

Question 37

Factor
-8x²y² + 32yz + 40y

Accepted Answer

8y(-x²y + 4z + 5)

Answer

8z(-x² + 4z +1)

Answer

8y(-4x²y² + 16yz + 20y)

Answer

4y (-2x²y + 40z + 10)

Question 38

Factor
8p³q⁴ - 3pq³m² + 6p³q²

Accepted Answer

pq²(8p²q² - 3m²q + 6p²)

Answer

pq²(8p²q³ - 3m²q² + 6p²q)

Answer

pq(32p²q² - 3m²q + 6p²)

Answer

4q²(8p²q² - 3m²q + 6p²)

Question 39

What is the greatest common factor of the three terms in the expression
-96xy - 144x - 84

Accepted Answer

-12

Answer

12x

Answer

-12xy

Answer

12

Question 40

What is the greatest common factor of the following polynomial:
-9xy - 81xy - 18 - 45xy

Accepted Answer

-9

Answer

9xy

Answer

9x

Answer

xy

GCF and Grouping Test

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