Find the greatest common factor (GCF/HCF) of the following polynomials:
2x^2and12x^2
6x^3y\ and\ 18x^2y^3
42x^2yz\ and\ 63x^3y^2z^3
12ax^2a^2x^3and2a^3x
9x^2,15x^2y^3,6xy^2and21x^2y^2
4a^2b^3,-12a^3b,18a^4b^3
6x^2y^2,9xy^3,3x^3y^2
a^2b^3,a^3b^2
36a^2b^2c^4,54a^5c^2,90a^4b^2c^2
x^3,-yx^2
15a^3,-45a^2,-150a
2x^3y^2,10x^2y^3,14xy
14x^3y^5,10x^5y^3,2x^2y^2
Find the greatest common factor of the terms in each of the following expressions:
5a4 + 10a3 – 15a2
2xyz + 3x2y + 4y2
3a2b2 + 4b2c2 + 12a2b2c2
Factorize the following:
3x – 9
5x – 15x2
20a12b2 – 15a8b4
72x6y7 – 96x7y6
20x3 – 40x2 + 80x
2x3y2 – 4x2y3 + 8xy4
10m3n2 + 15m4n – 20m2n3
2a4b4 – 3a3b5 + 4a2b5
28a2 + 14a2b2 – 21a4
a4b – 3a2b2 – 6ab3
212mn – 3lm2n + 4lmn2
x4y2 – x2y4 – x4y4
9x2y + 3axy
16m – 4m2
-4a2 + 4ab – 4ca
x2yz + xy2z + xyz2
ax2y + bxy2 + cxyz
Factorize each of the following algebraic expressions:
6x (2x – y) + 7y (2x – y)
2r (y – x) + s (x – y)
7a (2x – 3) + 3b (2x – 3)
9a (6a – 5b) – 12a2 (6a – 5b)
5 (x – 2y)2 + 3 (x – 2y)
16 (2l – 3m)2 – 12 (3m – 2l)
3a (x – 2y) – b (x – 2y)
a2 (x + y) + b2 (x + y) + c2 (x + y)
(x – y)2 + (x – y)
6 (a + 2b) – 4 (a + 2b)2
a (x – y) + 2b (y – x) + c (x – y)2
-4 (x – 2y)2 + 8 (x – 2y)
x3 (a – 2b) + x2 (a – 2b)
(2x – 3y) (a + b) + (3x – 2y) (a + b)
4(x + y) (3a – b) + 6(x + y) (2b – 3a)
Factorize each of the following expressions:
qr – pr + qs – ps
p2q – pr2 – pq + r2
1 + x + xy + x2y
ax + ay – bx – by
xa2 + xb2 – ya2 – yb2
x2 + xy + xz + yz
2ax + bx + 2ay + by
ab – by – ay + y2
axy + bcxy – az – bcz
lm2 – mn2 – lm + n2
x3 – y2 + x – x2y2
6xy + 6 – 9y – 4x
x2 – 2ax – 2ab + bx
x3 – 2x2y + 3xy2 – 6y3
abx2 + (ay – b) x – y
(ax + by)2 + (bx – ay)2
16 (a – b)3 – 24 (a – b)2
ab (x2 + 1) + x (a2 + b2)
a2x2 + (ax2 + 1)x + a
a (a – 2b – c) + 2bc
a (a + b – c) – bc
x2 – 11xy – x + 11y
ab – a – b + 1
x2 + y – xy – x
16x2 – 25y2
27x2 – 12y2
144a2 – 289b2
12m2 – 27
125x2 – 45y2
144a2 – 169b2
(2a – b)2 – 16c2
(x + 2y)2 – 4 (2x – y)2
3a5 – 48a3
a4 – 16b4
x8 – 1
64 – (a + 1)2
36l2 – (m + n)2
25x4y4 – 1
a4 – 1/b4
x3 – 144x
(x – 4y)2 – 625
9 (a – b)2 – 100 (x – y)2
(3 + 2a)2 – 25a2
(x + y)2 – (a – b)2
1/16x2y2 – 4/49y2z2
75a3b2 – 108ab4
x5 – 16x3
50/x2 – 2x2/81
256x3 – 81x
a4 – (2b + c)4
(3x + 4y)4 – x4
p2q2 – p4q4
3x3y – 24xy3
a4b4 – 16c4
x4 – 625
x4 – 1
49(a – b)2 – 25(a + b)2
x – y – x2 + y2
16(2x – 1)2 – 25y2
4(xy + 1)2 – 9(x – 1)2
(2x + 1)2 – 9x4
x4 – (2y – 3z)2
a4 – b2 + a – b
16a4 – b4
a4 – 16(b – c)4
2a4 – 32a
a4b4 – 81c4
xy9 – yx9
x3 – x
18a2x2 – 32
4x2 + 12xy + 9y2
9a2 – 24ab + 16b2
p2q2 – 6pqr + 9r2
36a2 + 36a + 9
a2 + 2ab + b2 – 16
9z2 – x2 + 4xy – 4y2
16 – a6 + 4a3b3 – 4b6
a2 – 2ab + b2 – c2
x2 + 2x + 1 – 9y2
a2 + 4ab + 3b2
96 – 4x – x2
a4 + 3a2 + 4
4x4 + 1
4x4 + y4
(x + 2)4 – 6(x + 2) + 9
25 – p2 – q2 – 2pq
x2 + 9y2 – 6xy – 25a2
49 – a2 + 8ab – 16b2
a2 – 8ab + 16b2 – 25c2
x2 – y2 + 6y – 9
25x2 – 10x + 1 – 36y2
a2 – b2 + 2bc – c2
a4 + 2b + b2 – c2
49 – x2 – y2 + 2xy
a2 + 4b2 – 4ab – 4c2
x2 – y2 – 4xz + 4z2
x2 + 12x – 45
40 + 3x – x2
a2 + 3a – 88
a2 – 14a – 51
x2 + 14x + 45
x2 – 22x + 120
x2 – 11x – 42
a2 + 2a – 3
a2 + 14a + 48
x2 – 4x – 21
y2 + 5y – 36
(a2 – 5a)2 – 36
(a + 7) (a – 10) + 16
Resolve each of the following quadratic trinomials into factors:
2x2 + 5x + 3
2x2 – 3x – 2
3x2 + 10x + 3
7x – 6 – 2x2
7x2 – 19x – 6
28 – 31x – 5x2
3 + 23y – 8y2
11x2 – 54x + 63
7x – 6x2 + 20
3x2 + 22x + 35
12x2 – 17xy + 6y2
6x2 – 5xy – 6y2
6x2 – 13xy + 2y2
14x2 + 11xy – 15y2
6a2 + 17ab – 3b2
36a2 + 12abc – 15b2c2
15x2 – 16xyz – 15y2z2
(x – 2y)2 – 5 (x – 2y) + 6
(2a – b)2 + 2 (2a – b) – 8
Factorize each of the following quadratic polynomials by using the method of completing the square:
p2 + 6p + 8
**Factorize each of the following quadratic polynomials by using the method of
completing the square:**
q2 – 10q + 21
4y2 + 12y + 5
p2 + 6p – 16
x2 + 12x + 20
4x2 – 12x + 5
y2 – 7y + 12
z2 – 4z – 12
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