Question

exercicile1,2,3,4va rogggg

Answer 1

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

E)
$(8 - 3x) + (10x - 7)(3x - 8) = \\ - ( 3x - 8) + (10x - 7)(3x - 8) \\ (3x - 8)( - 1 + 10x - 7) = \\ (3x - 8)(10x - 8)$
F)
$(6x - 5) - (14x - 9)(5 - 6x) = \\ (6x - 5) + (14x - 9)(6x - 5) = \\ (6x - 5)(1 + 14x - 9) = \\ (6x - 5)(14x - 8)$

4)a)
$(2x - 3)(3 - x) + \\ (2x - 3)(4x - 1) = \\ (2x - 3)(3 - x + 4x - 1) = \\ (2x - 3)(3x + 2)$
B)
$(x - 2)(4x - 15) - \\ (2 - 3x)(x - 2) = \\ (x - 2)(4x - 15 - 2 + 3x) = \\ (x - 2)(7x - 17)$
C)
$(5x - 1)(x + 6) - \\ (4x + 5)(5x - 1) = \\ (5x - 1)(x + 6 - 4x - 5) = \\ (5x - 1)( - 3x + 1)$
D)
$(2x - 7)(5 - 3x) - \\ (5 - 3x)(x - 8) = \\ - (2x - 7)(3x - 5) + \\ (3x - 5)(x - 8) = \\ (3x - 5)( - 2x + 7 + x - 8) =$
$= (3x - 5)( - x - 1)$

E)
$(1 - 3x)(7x + 2) - \\ (3x - 1)(5 - 2x) = \\ - (3x - 1)(7x + 2) - \\ (3x - 1)(5 - 2x) =$
$(3x - 1)( - 7x - 2 - 5 + 2x) = \\ (3x - 1)( - 5x - 7)$
F)
$(5 - 4x)(6x - 1) + \\ (5x + 3)(4x - 5) = \\ - (4x - 5)(6x - 1) + \\ (5x + 3)(4x - 5) =$
$(4x - 5)($-6x+1+5x+3)=(4x-5)(-x+4)
Sper ca e bine!