1)A)
[tex] {14x}^{5} + {2x}^{3} = 2 {x}^{3} ( {7x}^{2} + 1)[/tex]
B)
[tex] {12x}^{6} - {8x}^{3} = 4 {x}^{3} ( {3x}^{3} -2 ) [/tex]
C)
[tex] {6x}^{4} + {15x}^{2} = {3x}^{2}( {2x}^{2} + 5)[/tex]
D)
[tex] {10x}^{7} + {15x}^{6} = {5x}^{6} (2x + 3)[/tex]
E)
[tex] {14x}^{9} - {21x}^{6} = {7x}^{6} ( {2x}^{3} - 3)[/tex]
F)
[tex] {12x}^{8} - {21x}^{4} = {3x}^{4} ( {4x}^{4} - 7)[/tex]
G)
[tex] {18x}^{6} - {42x}^{3} = {6x}^{3} ( {3x}^{3} - 7)[/tex]
H)
[tex] {24x}^{5} + {40x}^{2} = {4x}^{2} ( {6x}^{3} + 10)[/tex]
I)
[tex] {63x}^{5} - {27x}^{3} = {9x}^{3} ( {7x}^{2} - 3)[/tex]
2)a)
[tex] {20x}^{8} - {25x}^{7} - {10x}^{4} = \\ {5x}^{4} ( {4x}^{4} - {5x}^{3} - 2)[/tex]
B)
[tex] {30x}^{9} - {24x}^{6} + {18x}^{5} = \\ {6x}^{5}( {5x}^{4} - 4x + 3)[/tex]
C)
[tex] {21x}^{9} - {14x}^{8} - {28x}^{5} = \\ {7x}^{5} ( {3x}^{4} - {2x}^{3} - 4) [/tex]
D)
[tex] {27x}^{6} - {45x}^{5} - {15x}^{4} = \\ {3x}^{4} ( {9x}^{2} - 15x - 5)[/tex]
E)
[tex] - {28x}^{4} - {36x}^{3} - {20x}^{2} = \\ {2x}^{2} ( - {14x}^{2} - 18x - 10)[/tex]
F)
[tex] - {18x}^{8} - {45x}^{5} + {63x}^{4} = \\ {3x}^{4} ( - {6x}^{4} - 15x + 21)[/tex]
3)a) [tex](x - 3)(4x - 5) + 2(x - 3) = \\ (x - 3)(4x - 5 + 2) = \\ (x - 3)(4x - 3)[/tex]
B)
[tex](x + 5)(2x + 7) - 4(x + 5) = \\ (x + 5)(2x + 7 - 4) = \\ (x + 5)(2x + 3)[/tex]
C)
[tex](4x + 1)(x - 7) + 6(4x + 1) = \\ (4x + 1)(x - 7 + 6) = \\ (4x + 1)(x - 1)[/tex]
D)
[tex](7x - 1)(x + 9) - 6(7x - 1) = \\ (7x - 1)(x + 9 - 6) = \\ (7x - 1)(x + 3)[/tex]
E)
[tex](8 - 3x) + (10x - 7)(3x - 8) = \\ - ( 3x - 8) + (10x - 7)(3x - 8) \\ (3x - 8)( - 1 + 10x - 7) = \\ (3x - 8)(10x - 8)[/tex]
F)
[tex](6x - 5) - (14x - 9)(5 - 6x) = \\ (6x - 5) + (14x - 9)(6x - 5) = \\ (6x - 5)(1 + 14x - 9) = \\ (6x - 5)(14x - 8)[/tex]
4)a)
[tex](2x - 3)(3 - x) + \\ (2x - 3)(4x - 1) = \\ (2x - 3)(3 - x + 4x - 1) = \\ (2x - 3)(3x + 2)[/tex]
B)
[tex](x - 2)(4x - 15) - \\ (2 - 3x)(x - 2) = \\ (x - 2)(4x - 15 - 2 + 3x) = \\ (x - 2)(7x - 17)[/tex]
C)
[tex](5x - 1)(x + 6) - \\ (4x + 5)(5x - 1) = \\ (5x - 1)(x + 6 - 4x - 5) = \\ (5x - 1)( - 3x + 1)[/tex]
D)
[tex](2x - 7)(5 - 3x) - \\ (5 - 3x)(x - 8) = \\ - (2x - 7)(3x - 5) + \\ (3x - 5)(x - 8) = \\ (3x - 5)( - 2x + 7 + x - 8) = [/tex]
[tex] = (3x - 5)( - x - 1)[/tex]
E)
[tex](1 - 3x)(7x + 2) - \\ (3x - 1)(5 - 2x) = \\ - (3x - 1)(7x + 2) - \\ (3x - 1)(5 - 2x) = \\ [/tex]
[tex](3x - 1)( - 7x - 2 - 5 + 2x) = \\ (3x - 1)( - 5x - 7)[/tex]
F)
[tex](5 - 4x)(6x - 1) + \\ (5x + 3)(4x - 5) = \\ - (4x - 5)(6x - 1) + \\ (5x + 3)(4x - 5) = [/tex]
[tex](4x - 5)([/tex]-6x+1+5x+3)=(4x-5)(-x+4)
Sper ca e bine!
