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WorksheetsFactoring - All Techniques
Total questions: 131
Worksheet time: 7hrs 19mins
What is the greatest common factor of 30x and 56x2
4x
6x
2x
x
What is 144x3 written in prime factorization form?
12*12*x*x*x
2*2*2*2*3*3*x*x*x
2*2*2*3*3*3*x*x*x
2*2*12*x*x*x
Find the GCF of the following terms;
5xy3z ; 26x2y5z2 ; 10x3yz2
5xyz
x2y3z5
2xy3z
xyz
24m3n5p + 6mn4p2 + 4mn5
The GCF of 24, 36, and 72 is.....
12
18
36
24
What is the prime factorization of the number 60?
4 x 3 x 5
2 x 2 x 3 x 5
2 x 3 x 3 x 5
2 x 3 x 1 0
What is the GCF of 18 and 45?
3
12
9
6
The common factors of 16 and 24 are....
2, 4 and 8
2, 4, 12, and 24
1, 2, 4 and 8
2, 4 and 8
The GCF of 42, 98, and 182 is....
2
14
7
21
Multiply 5x(2x + 3)
10x2 + 15x
7x + 15x
7x2 + 8x
25x2
4x2 - 64y2
Prime
( 2x - 32y) (2 x + 32y)
4( 2x - 8y) (2 x - 8y)
4( x + 4y) (x - 4y)
What is the factor of x2 - 9?
x+3
(x+3)(x-3)
(x-3)(x-3)
x-3
What is the factor of 4x2 - 64?
2x-8(8)
(2x+8)(2x-8)
(x+8)(x-8)
4(x -16)
The pattern
x3−y3 is called a/an _________.Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
Square of a Binomial
What must ALWAYS be done before factoring polynomials?
Factor the difference of two squares
Look for the value of the variables
Find the values of a, b and c
Look for the Greatest Common Factor (GCF)
The binomial
Difference of Two Squares
Sum of Two Cubes
Difference of Two Cubes
Square of a Binomial
Factoring the sum or difference of two cubes can be used ONLY if the two terms of the binomials have perfect square roots.
TRUE
FALSE
Factor completely 64x6+y6
(4x2+y2)(16x4−4x2y2−y4)
(4x2−y2)(16x4+4x2y2+y4)
(4x2+y2)(16x4−4x2y2+y4)
(4x2−y2)(16x4−4x2y2−y4)
To get the cube root of a variable with exponent, divide the exponent by three and raise it to the same base.
TRUE
FALSE
Factor 27x3−64
(3x+4)(9x2−12x+16)
(3x+4)(9x2+12x+16)
(3x−4)(9x2−12x+16)
(3x−4)(9x2+12x+16)
Which of the following is the complete factored form of x3y9+1000
(xy3+10)(x2y6−10xy3+100)
(xy+10)(x2y2−10xy+100)
(xy3−10)(x2y6+10xy3+100)
(xy3−10)(x2y6−20xy3+100)
What must be multiplied to (5x2+2y) to get a product of 125x6+8y3 ?
(5x2+2y)
(5x2−2y)
(5x4+10x2y+2y2)
(25x4−10x2y+4y2)
Factor completely.
x2 - 144
( x - 12 ) 2
( x - 12 ) ( x - 12 )
( x + 12 ) ( x + 12 )
( x + 12 ) ( x - 12 )
Factor completely.
y2 - 196
( y - 14 ) ( y - 14 )
( y + 14 ) ( y - 14 )
( y + 13 ) ( y - 13 )
( y - 13 ) 2
Factor completely.
121x2 - 49
( 11x - 7 ) 2
( 11x - 7 ) ( 11x - 7 )
( 11x + 7 ) ( 11x - 7 )
( 12x + 7 ) ( 12x - 7 )
Factor completely.
64x2 - 49y2
( 8x + 7 ) ( 8x - 7 )
( 8x - 7y ) ( 8x - 7y )
( 8x + 7y ) ( 8x - 7y )
( 8x - 7y )2
Factor completely.
225x2 - 169y2
( 15x - 13y )2
( 15x + 13 ) ( 15x - 13 )
( 25x + 13y ) ( 25x - 13y )
( 15x + 13y ) ( 15x - 13y )
What is ALWAYS the first step when factoring?
Look for the GCF
Write a, b, and c
Difference of squares
Use the X-Puzzle
Which of these can factor using difference of two squares?
144x2 - 49y2
x2 + 4x - 12
100x2 + 20x + 1
14x - 16
Which one is false about the difference of two squares?
We can factor because there is addition sign.
We can factor because there is a perfect squared number (Example: x2, 25, 49)
Formula: a2 - b2 = (a + b) (a - b)
We can factor because there is minus sign.
We can't factor using difference of two square this
49x2 + 4y2. Why?
Because 4 is not a perfect cubed number.
Because 4 is not a perfect squared number.
Because 49 is not a perfect squared number.
Because we can't factor using difference of two squares if it is addition sign.
Factor 4x2-9
(4x-9)(4x+9)
(2x-3)(2x+3)
2x-3
(2x-4.5)(2x+4.5)
Factor x2-25
( x + 5 ) ( x - 5 )
( x - 5 ) ( x - 5 )
( x + 5 ) ( x + 5 )
Prime
Factor completely.
121x2 - 49
( 11x - 7 ) 2
( 11x - 7 ) ( 11x - 7 )
( 11x + 7 ) ( 11x - 7 )
( 12x + 7 ) ( 12x - 7 )
25x2-81
(Check for a GCF)
(Check for a GCF)
Factor
x2 + 18x + 81
(x + 9)(x – 9)
(x + 18)2
(x + 9)2
(x + 6)2
Factor: x2 - 20x + 100
(x-10)2
(x+10)2
n2 + 10n + 25
x2 + 16x + 64
x2 + 18x + 9
x2 + 14x + 49
x2 + 16x + 64
x2 + 14x + 49
x2 + 6x + 9
x2 + 18x + 9
x2 + 10x + 100
n2 + 10n + 25
x2 + 18x + 81
Is a2 − 20a + 100 a perfect square trinomial?
No
Yes
Cannot be identfied
Is 4x2 − 12x + 8 a perfect square trinomial?
No
Yes
Cannot be identfied
Factor 4x2 − 12x + 9 completely
(2x −3)2
(2x +3)2
(2x −3)(2x + 3)
Cannot be SOLVED
Factor p2 +24p + 144
(p + 12)2
(p −12)2
(p − 12)(P + 12)
(p −12)(p−12)
Factor a2−18a +81
(a−9)(a−9)
(a+9)(a+9)
(a − 9)(a + 9)
CANNOT BE SOLVED
Factor x2−4x+4
(x−2)2
(x−4)2
(x+2)(x+2)
(x−2)(x+2)
Factor a2+30ab + 225b2
(a+15b)2
(a−15b)2
(a−15b)(a+15b)
(a+15)(a+15b2)
Factor x2 +10x + 25
(x+5)(x+5)
(x−5)(x−5)
(x−5)(x+5)
(x2+5)(1+5)
Is this x2 +50x + 625 a perfect square trinomial?
Yes
No
Cannot be Identified
Factor (m4−18m2+81) completely
(m+3)(m−3)(m2+9)
(m2−9)(m2+9)
(m−3)(m−3)(m+3)(m+3)
(m+3)(m−3)(m2−9)
Factor
k2+7k+10 .(k+2)(k−5)
(k+2)(k+5)
(k+10)(k+4)
(k−2)(k−5)
Factor k2−2k−24
(k−4)(k+6)
(k+4)(k+6)
(k+6)(k−1)
(k+4)(k−6)
Factor x2+9x−36
(x+12)(x−3)
(x+9)(x−4)
(x−9)(x−4)
(x−12)(x+3)
r2 -16r + 60
Factor completely: 3a2+4a+1
(3a−1)(a−1)
(3a+1)(a+1)
(3a−1)(a+1)
Prime
Factor completely: 3n2−15n+18
(x−12)(x+3)
(3n−9)(n−2)
3(n−3)(n−2)
3(n+2)(n+3)
What do we ALWAYS need to do first before factoring polynomials?
Find the values of a, b and c
Look for the value of the variables
Factor the factors of c that the sum is b
Look for the Greatest Common Factor
What is the GCF of the trinomial?
3x2 - 9x -120
2
3
6
9
To factor
x2+8x+15 , find two factors of 15 whose sum is _____.1
2
8
15
To factor
x2−10−24 , which of the following factors of −24 must be chosen in the process?−2, 12
−6, −4
2, −12
−6, 4
What are the factors of x2+10x+21?
(x+21)(x+1)
(x-21)(x-1)
(x+7)(x+3)
(x-7)(x-3)
What are the factors of m2-16m+63?
(m+9)(m+7)
(m-9)(m-7)
(m+21)(m+3)
(m-21)(m-3)
What are the factors of t2+2t-24?
(t+4)(t-6)
(t+6)(t-4)
(t-8)(t+3)
(t-3)(t+8)
What are the factors of 7p2+36p+32?
(7p-8)(p+4)
(7p+8)(p-4)
(7p-8)(p-4)
(7p+8)(p+4)
What are the factors of 12y2+7y-10?
(3y+2)(4y-5)
(3y-2)(4y+5)
(12y-10)(y+1)
(12y+10)(y-1)
3x2 + 18x +15
Hint: Factor GCF first.
3a2 + 4a + 1
3v2 - 4v - 7
2m² + 3m - 9
Factor Completely
v2+11v+28
(v−7)(v+4)
(v+7)(v−4)
(v+6)(v+3)
(v+7)(v+4)
x2−5x+6 Factor Completely
(x−3)(x−2)
(x+3)(x−2)
x(x−10)
(x−3)(x+2)
Factor Completely
m2+11m+10
4(m−3)(m+10)
(m+10)(m−1)
(m+10)(m+1)
(m−10)(m+1)
10. Give the complete factorization of 4n2−16n−48
(4n-6)(n+2)
(n-6)(4n+2)
4(n-6)(n+2)
What are the factors of 12y2+7y-10?
(3y+2)(4y-5)
(3y-2)(4y+5)
(12y-10)(y+1)
(12y+10)(y-1)
What are the factors of 7p2+36p+32?
(7p-8)(p+4)
(7p+8)(p-4)
(7p-8)(p-4)
(7p+8)(p+4)
Factor by grouping:
x3−4x2−4x+16
(x+4)(x+2)
(x−4)(x2−4)
(x+4)(x2−4)
(x−4)(x−2)
Factor by grouping:
(2p2+3)(p+2)
(2p2+6)(p+4)
(4p2+3)(p+2)
(4p2+8p)(3p+6)
Factor by grouping:
(x2−2)(x−7)
(x2+2)(x+7)
(x2+2)(x−7)
(x2−2)(x+7)
What is the factored form of 5n3−10n2+3n−6 ?
(5n2+3)(n−2)
(5n2−3)(n−2)
(5n3+3)(n−2)
10n(n2−6)
Which of the following would be part of the factored form of x3−2x2+5x+10 ?
(x−2)
(x+2)
(x2+5)
(x2−5)
If I were to factor 6n3+3n2+8n+4 by grouping, my answer would look like (3n2+4) times what other binomial?
(a)
Factor by grouping:
x3−5x2+5x−25
(x2−5)(x−5)
(x2+5)(x−5)
(x2−5)(x+5)
(x2+5)(x+5)
Which of the following would be part of the factored form of x3−3x2+2x−6 ?
(x−3)
(x+3)
(x2+2)
(x2−2)
Factor by grouping:
20p3−25p2+4p−5
(5p2−1)(4p−5)
(5p2+1)(4p+5)
(5p2+1)(4p−5)
(5p2−1)(4p+5)
Is (5x−4) a factor of 5x3−4x2−25x+20 ?
Yes, it is a factor.
No, it is not a factor.
What is the factored form of x³+7x²-2x-14
(x²-2)(x-7)
(x²+2)(x-7)
(x²+2)(x+7)
(x²-2)(x+7)
(3x³+9x²-2x)−(7x³-6x²+1)
(x+2)(x-5)
(y+6)(6y²+9y-8)
