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WorksheetsFactoring Polynomials
Total questions: 20
Worksheet time: 10mins
What is the process of finding the factors of an expression which is the reverse process of multiplication?
rationalization
special product
continuous division
factoring
Refers to the common factor having the greatest numerical factor and with variables having the least degree.
Least Common Multiple
Greatest Common Factor
Perfect Square
Difference of two squares
What is the Greatest Common Factor of 24 and 54?
2
4
6
8
What is the GCF of 20, 24, and 40?
1
4
8
10
What is the GCF of 𝑥 2 and 𝑥 9 ?
x2
x7
x11
x9
What are the complete factors of the polynomial 7𝑥 − 7?
7(𝑥 − 1)
7(1 − x)
7𝑥 – 1
7(𝑥 − 7)
Which of the following pair of numbers has a GCF of 6?
2 and 3
8 and 12
6 and 10
12 and 18
All of the following are factors of 12x2 except one. What is it?
12
12x
12x2
12x3
What is the GCF of 2a3 and a 6?
a3
2a3
a6
2a6
What is the GCF of 𝑥𝑦 10 ,𝑥 4𝑦 6 , 𝑥 9𝑦 9 , and 𝑥 10𝑦 10?
xy
xy6
x4y4
x4y6
If one factor of 4x2 + 6 is 2, what is the other factor?
2x + 3
4x + 6
2x + 6
2x2 + 3
If one factor of 6ab2 – 12 a2b 3 is 1 – 2ab, what is the other factor?
6ab
6a2b
6ab2
6a2b 2
Which of the following expressions has factors (2x - y) and (2x + y)?
2x2 + y2
4x2 – y 2
2x2 – y 2
2x2 – y 2
Using the pattern for factoring the sum of cubes, we know that factoring 8 + 𝑏 3 gives
(2 − 𝑏)(4 − 2𝑏 + 𝑏 2 )
(2 + 𝑏)(4 − 2𝑏 + 𝑏 2 )
(2 − 𝑏)(4 + 2𝑏 + 𝑏 2 )
(2 + 𝑏)(4 + 2𝑏 + 𝑏 2 )
What is the complete factored form of 27𝑥 3 – 64𝑦 3?
(3x – 4y)
(9x2 + 12xy + 16y2 )
(3x – 4y)
(9x2 - 12xy + 16y2 )
(3x + 4y)
(9x2 - 12xy + 16y2 )
(3x + 4y)
(9x2 + 12xy + 16y2 )
What is the complete factored form of 10 + 270y3?
10(1 + 3y)
(1 + 3y +9y2 )
10(1 + 3y)
(1 - 3y +9y2 )
10(1 - 3y)
(1 + 3y +9y2 )
10(1 - 3y)
(1 - 3y +9y2 )
Your classmate was asked to square (2𝑥 – 3), he answered 4𝑥 2 − 9. Is his answer correct?
Yes, because product rule is correctly applied.
Yes, because squaring a binomial always produces a binomial product.
No, because the answer must be 4𝑥 2 + 9.
No, because squaring a binomial always produces a trinomial product.
What is the complete factored form of the expression 𝑦 4 − 49?
(𝑦 2 ) 2 − (7 2 ) 2
(𝑦 2 − 7) 2
(𝑦 2 + 7) 2
(𝑦 2 − 7) (𝑦 2 + 7)
The area of a rectangular garden is 9t2 – 64 square units. If one side is 3t – 8, what is the other side?
3t - 8
3t + 8
t - 8
t + 8
We use the following properties or identities to factor polynomials except,
Difference of Two Squares
Sum and Difference of two cubes
Greatest Common Factor
None of the choices
