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Worksheets

Factoring Polynomials

Total questions: 20

Worksheet time: 10mins

Name
Class
Date
1.

What is the process of finding the factors of an expression which is the reverse process of multiplication?

a)

rationalization

b)

special product

c)

continuous division

d)

factoring

2.

Refers to the common factor having the greatest numerical factor and with variables having the least degree.

a)

Least Common Multiple

b)

Greatest Common Factor

c)

Perfect Square

d)

Difference of two squares

3.

What is the Greatest Common Factor of 24 and 54?

a)

2

b)

4

c)

6

d)

8

4.

What is the GCF of 20, 24, and 40?

a)

1

b)

4

c)

8

d)

10

5.

What is the GCF of 𝑥 2 and 𝑥 9 ?

a)

x2

b)

x7

c)

x11

d)

x9

6.

What are the complete factors of the polynomial 7𝑥 − 7?

a)

7(𝑥 − 1)

b)

7(1 − x)

c)

7𝑥 – 1

d)

7(𝑥 − 7)

7.

Which of the following pair of numbers has a GCF of 6?

a)

2 and 3

b)

8 and 12

c)

6 and 10

d)

12 and 18

8.

All of the following are factors of 12x2 except one. What is it?

a)

12

b)

12x

c)

12x2

d)

12x3

9.

What is the GCF of 2a3 and a 6?

a)

a3

b)

2a3

c)

a6

d)

2a6

10.

What is the GCF of 𝑥𝑦 10 ,𝑥 4𝑦 6 , 𝑥 9𝑦 9 , and 𝑥 10𝑦 10?

a)

xy

b)

xy6

c)

x4y4

d)

x4y6

11.

If one factor of 4x2 + 6 is 2, what is the other factor?

a)

2x + 3

b)

4x + 6

c)

2x + 6

d)

2x2 + 3

12.

If one factor of 6ab2 – 12 a2b 3 is 1 – 2ab, what is the other factor?

a)

6ab

b)

6a2b

c)

6ab2

d)

6a2b 2

13.

Which of the following expressions has factors (2x - y) and (2x + y)?

a)

2x2 + y2

b)

4x2 – y 2

c)

2x2 – y 2

d)

2x2 – y 2

14.

Using the pattern for factoring the sum of cubes, we know that factoring 8 + 𝑏 3 gives

a)

(2 − 𝑏)(4 − 2𝑏 + 𝑏 2 )

b)

(2 + 𝑏)(4 − 2𝑏 + 𝑏 2 )

c)

(2 − 𝑏)(4 + 2𝑏 + 𝑏 2 )

d)

(2 + 𝑏)(4 + 2𝑏 + 𝑏 2 )

15.

What is the complete factored form of 27𝑥 3 – 64𝑦 3?

a)

(3x – 4y)

(9x2 + 12xy + 16y2 )

b)

(3x – 4y)

(9x2 - 12xy + 16y2 )

c)

(3x + 4y)

(9x2 - 12xy + 16y2 )

d)

(3x + 4y)

(9x2 + 12xy + 16y2 )

16.

What is the complete factored form of 10 + 270y3?

a)

10(1 + 3y)

(1 + 3y +9y2 )

b)

10(1 + 3y)

(1 - 3y +9y2 )

c)

10(1 - 3y)

(1 + 3y +9y2 )

d)

10(1 - 3y)

(1 - 3y +9y2 )

17.

Your classmate was asked to square (2𝑥 – 3), he answered 4𝑥 2 − 9. Is his answer correct?

a)

Yes, because product rule is correctly applied.

b)

Yes, because squaring a binomial always produces a binomial product.

c)

No, because the answer must be 4𝑥 2 + 9.

d)

No, because squaring a binomial always produces a trinomial product.

18.

What is the complete factored form of the expression 𝑦 4 − 49?

a)

(𝑦 2 ) 2 − (7 2 ) 2

b)

(𝑦 2 − 7) 2

c)

(𝑦 2 + 7) 2

d)

(𝑦 2 − 7) (𝑦 2 + 7)

19.

The area of a rectangular garden is 9t2 – 64 square units. If one side is 3t – 8, what is the other side?

a)

3t - 8

b)

3t + 8

c)

t - 8

d)

t + 8

20.

We use the following properties or identities to factor polynomials except,

a)

Difference of Two Squares

b)

Sum and Difference of two cubes

c)

Greatest Common Factor

d)

None of the choices